Samir Khan: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=613
en-us2021 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemTue, 26 Jan 2021 03:29:21 GMTTue, 26 Jan 2021 03:29:21 GMTNew applications published by Samir Khanhttps://www.maplesoft.com/images/Application_center_hp.jpgSamir Khan: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=613
Zero Padding a Signal to More Accurately Estimate Amplitudes from a DFT
https://www.maplesoft.com/applications/view.aspx?SID=154653&ref=Feed
You can use a discrete Fourier transform (DFT) to identify the amplitude of a sinusoidal signal. Given a signal with N samples and a sample rate of Fs, the frequency spacing of its DFT is Fs/N. An amplitude at a frequency that falls in a DFT bin can be accurately estimated.
<BR><BR>
But what if a signal frequency falls between DFT bins? Its energy will be shared between the adjacent bins, and its amplitude will not be accurately identified.
<BR><BR>
One possible solution to better amplitude estimation is zero padding the time domain signal. If you zero-pad the signal, the value of N increases, and the frequency spacing of the DFT decreases. For example, if you double the time-domain signal with zero-padding, the frequency spacing decreases by a factor of two.
<BR><BR>
This is not a magical way of increasing the sampling rate, or injecting more data. Zero-padding in the time domain is simply equivalent to sinc interpolation of the DFT.
<BR><BR>
In this application, we will
<UL>
<LI>generate a sinusoidal signal with three frequencies at three amplitudes (one frequency will fall in a DFT bin, but two won't)
<LI>use a DFT to estimate the signal amplitudes
<LI>zero-pad the original signal
<LI>use a DFT of the zero-padded signal to again estimate the amplitudes
</UL>
You will see that zero-padding the signal results in better amplitude estimation.<img src="https://www.maplesoft.com/view.aspx?si=154653/thumb.png" alt="Zero Padding a Signal to More Accurately Estimate Amplitudes from a DFT" style="max-width: 25%;" align="left"/>You can use a discrete Fourier transform (DFT) to identify the amplitude of a sinusoidal signal. Given a signal with N samples and a sample rate of Fs, the frequency spacing of its DFT is Fs/N. An amplitude at a frequency that falls in a DFT bin can be accurately estimated.
<BR><BR>
But what if a signal frequency falls between DFT bins? Its energy will be shared between the adjacent bins, and its amplitude will not be accurately identified.
<BR><BR>
One possible solution to better amplitude estimation is zero padding the time domain signal. If you zero-pad the signal, the value of N increases, and the frequency spacing of the DFT decreases. For example, if you double the time-domain signal with zero-padding, the frequency spacing decreases by a factor of two.
<BR><BR>
This is not a magical way of increasing the sampling rate, or injecting more data. Zero-padding in the time domain is simply equivalent to sinc interpolation of the DFT.
<BR><BR>
In this application, we will
<UL>
<LI>generate a sinusoidal signal with three frequencies at three amplitudes (one frequency will fall in a DFT bin, but two won't)
<LI>use a DFT to estimate the signal amplitudes
<LI>zero-pad the original signal
<LI>use a DFT of the zero-padded signal to again estimate the amplitudes
</UL>
You will see that zero-padding the signal results in better amplitude estimation.https://www.maplesoft.com/applications/view.aspx?SID=154653&ref=FeedMon, 17 Aug 2020 04:00:00 ZSamir KhanSamir KhanThe Speed of Sound on Mars
https://www.maplesoft.com/applications/view.aspx?SID=154652&ref=Feed
This application computes the speed of sound on Mars with the <A HREF="/support/help/Maple/view.aspx?path=ThermophysicalData/Property">ThermophysicalData:-Property</A> command. The application takes into account the atmospheric composition of Mars, and a recently recorded temperature at Elysium Planitia (the landing site of the Mars Insight).<img src="https://www.maplesoft.com/view.aspx?si=154652/THUMB.png" alt="The Speed of Sound on Mars" style="max-width: 25%;" align="left"/>This application computes the speed of sound on Mars with the <A HREF="/support/help/Maple/view.aspx?path=ThermophysicalData/Property">ThermophysicalData:-Property</A> command. The application takes into account the atmospheric composition of Mars, and a recently recorded temperature at Elysium Planitia (the landing site of the Mars Insight).https://www.maplesoft.com/applications/view.aspx?SID=154652&ref=FeedThu, 30 Jul 2020 04:00:00 ZSamir KhanSamir KhanTrajectory of a Bullet Using an Air Resistance Correlation
https://www.maplesoft.com/applications/view.aspx?SID=154651&ref=Feed
This application models the trajectory of a bullet fired from a gun. Specifically, the application numerically solves the differential equations that describe the motion of the bullet (assuming three degrees of freedom), together with a correlation for air resistance. The predictions are compared to manufacturer-supplied velocity-range data for a specific type of bullet; the model closely matches the manufacturer's data.<img src="https://www.maplesoft.com/view.aspx?si=154651/thumb2.png" alt="Trajectory of a Bullet Using an Air Resistance Correlation" style="max-width: 25%;" align="left"/>This application models the trajectory of a bullet fired from a gun. Specifically, the application numerically solves the differential equations that describe the motion of the bullet (assuming three degrees of freedom), together with a correlation for air resistance. The predictions are compared to manufacturer-supplied velocity-range data for a specific type of bullet; the model closely matches the manufacturer's data.https://www.maplesoft.com/applications/view.aspx?SID=154651&ref=FeedThu, 02 Jul 2020 04:00:00 ZSamir KhanSamir KhanVapor-Liquid Equilibrium of Benzene and Toluene
https://www.maplesoft.com/applications/view.aspx?SID=154649&ref=Feed
This application calculate the vapor-liquid equilibrium of a benzene-toluene mixture. Specifically, the application calculates the:
<UL>
<LI>temperature, given the composition of the liquid phase and pressure
<LI>dew point and composition of the liquid phase given composition of the vapor phase and pressure
</UL>
The application employs the empirical Antoine equation to calculate the vapor pressures of benzene and toluene. The parameters are sourced from the NIST Chemistry Webbook.
<BR><BR>
The techniques used here can be applied to many other mixtures - you just need to find the right data for the Antoine equation.<img src="https://www.maplesoft.com/view.aspx?si=154649/thumb.png" alt="Vapor-Liquid Equilibrium of Benzene and Toluene" style="max-width: 25%;" align="left"/>This application calculate the vapor-liquid equilibrium of a benzene-toluene mixture. Specifically, the application calculates the:
<UL>
<LI>temperature, given the composition of the liquid phase and pressure
<LI>dew point and composition of the liquid phase given composition of the vapor phase and pressure
</UL>
The application employs the empirical Antoine equation to calculate the vapor pressures of benzene and toluene. The parameters are sourced from the NIST Chemistry Webbook.
<BR><BR>
The techniques used here can be applied to many other mixtures - you just need to find the right data for the Antoine equation.https://www.maplesoft.com/applications/view.aspx?SID=154649&ref=FeedTue, 30 Jun 2020 04:00:00 ZSamir KhanSamir KhanHeat Transfer Coefficient and Critical Heat Flux for Nucleate Pool Boiling
https://www.maplesoft.com/applications/view.aspx?SID=154650&ref=Feed
This application computes the:
<UL><LI>heat transfer coefficient for nucleate pool boiling using the correlation published by Foster and Zuber (1955)
<LI>and actual and critical heat fluxes.
</UL>
If the actual heat flux is greater than the critical heat flux, a vapor film separates the liquid from rewetting the surface of the container. This decreases the efficiency of heat transfer.<img src="https://www.maplesoft.com/view.aspx?si=154650/thumb.png" alt="Heat Transfer Coefficient and Critical Heat Flux for Nucleate Pool Boiling" style="max-width: 25%;" align="left"/>This application computes the:
<UL><LI>heat transfer coefficient for nucleate pool boiling using the correlation published by Foster and Zuber (1955)
<LI>and actual and critical heat fluxes.
</UL>
If the actual heat flux is greater than the critical heat flux, a vapor film separates the liquid from rewetting the surface of the container. This decreases the efficiency of heat transfer.https://www.maplesoft.com/applications/view.aspx?SID=154650&ref=FeedTue, 30 Jun 2020 04:00:00 ZSamir KhanSamir KhanMinimum Road Radius for Highway Superelevation
https://www.maplesoft.com/applications/view.aspx?SID=154647&ref=Feed
When a vehicle travels around a curve, a centripetal force is needed to keep the vehicle on the road. If the road is completely horizontal, this force is entirely provided by side friction (i.e. the friction of the tires on the road).
<BR><BR>
However, road curves are usually banked - the outer edge is higher than the inner edge. This uses the weight of the vehicle to help keep the vehicle on the road, and is called superelevation.
<BR><BR>
In this application, we derive an equation that describes the relationship between velocity, side friction, road radius and superelevation for a point-mass vehicle traveling around a bend. This relationship is then rearranged to give an explicit equation for the road radius.
<BR><BR>
This equation is then used to calculate the road radius required to maintain the trajectory of a vehicle as it travels around a bend. For a specific set of parameters, the calculated road radius matches the minimum road radius given in the AASHTO Green Book.<img src="https://www.maplesoft.com/view.aspx?si=154647/superelevation.png" alt="Minimum Road Radius for Highway Superelevation" style="max-width: 25%;" align="left"/>When a vehicle travels around a curve, a centripetal force is needed to keep the vehicle on the road. If the road is completely horizontal, this force is entirely provided by side friction (i.e. the friction of the tires on the road).
<BR><BR>
However, road curves are usually banked - the outer edge is higher than the inner edge. This uses the weight of the vehicle to help keep the vehicle on the road, and is called superelevation.
<BR><BR>
In this application, we derive an equation that describes the relationship between velocity, side friction, road radius and superelevation for a point-mass vehicle traveling around a bend. This relationship is then rearranged to give an explicit equation for the road radius.
<BR><BR>
This equation is then used to calculate the road radius required to maintain the trajectory of a vehicle as it travels around a bend. For a specific set of parameters, the calculated road radius matches the minimum road radius given in the AASHTO Green Book.https://www.maplesoft.com/applications/view.aspx?SID=154647&ref=FeedWed, 03 Jun 2020 04:00:00 ZSamir KhanSamir KhanHighway Pavement Design using the CALTRANS method
https://www.maplesoft.com/applications/view.aspx?SID=154646&ref=Feed
A highway pavement is several layers of materials above the natural soil. This application helps you design a flexible pavement using the approach outlined in the Highway Design Manual (6th edition) published by the California Department of Transportation (CALTRANS). Specifically, this application will determine the thickness of the subbase, base and asphalt concrete layers.<img src="https://www.maplesoft.com/view.aspx?si=154646/caltrans_highway_pavement.png" alt="Highway Pavement Design using the CALTRANS method" style="max-width: 25%;" align="left"/>A highway pavement is several layers of materials above the natural soil. This application helps you design a flexible pavement using the approach outlined in the Highway Design Manual (6th edition) published by the California Department of Transportation (CALTRANS). Specifically, this application will determine the thickness of the subbase, base and asphalt concrete layers.https://www.maplesoft.com/applications/view.aspx?SID=154646&ref=FeedFri, 29 May 2020 04:00:00 ZSamir KhanSamir KhanVenting of Gas From a Hole in a Pipe
https://www.maplesoft.com/applications/view.aspx?SID=154644&ref=Feed
This application calculates the rate at which gas flows out of a hole (or throat) in a pressurized pipe. Additionally, the Mach number, gas temperature and velocity, and speed of sound at the throat are computed.
<BR><BR>
The same analysis can be applied to a pressurized tank venting gas through a hole, as long as the internal conditions are constant.
<BR><BR>
The hole is small compared to the pipe diameter (so that the gas vents at a greater rate than the bulk flow of gas through the pipe), and the process is at steady-state and isentropic.
<BR><BR>
The polytropic coefficient and molecular weight of the gas are computed with the <A HREF="/support/help/maple/view.aspx?path=ThermophysicalData">ThermophysicalData package</A>.<img src="https://www.maplesoft.com/view.aspx?si=154644/Venting_of_Gas_from_a_Hole_in_a_Pipe.png" alt="Venting of Gas From a Hole in a Pipe" style="max-width: 25%;" align="left"/>This application calculates the rate at which gas flows out of a hole (or throat) in a pressurized pipe. Additionally, the Mach number, gas temperature and velocity, and speed of sound at the throat are computed.
<BR><BR>
The same analysis can be applied to a pressurized tank venting gas through a hole, as long as the internal conditions are constant.
<BR><BR>
The hole is small compared to the pipe diameter (so that the gas vents at a greater rate than the bulk flow of gas through the pipe), and the process is at steady-state and isentropic.
<BR><BR>
The polytropic coefficient and molecular weight of the gas are computed with the <A HREF="/support/help/maple/view.aspx?path=ThermophysicalData">ThermophysicalData package</A>.https://www.maplesoft.com/applications/view.aspx?SID=154644&ref=FeedMon, 25 May 2020 04:00:00 ZSamir KhanSamir KhanSpatially Varied Open-Channel Flow with Increasing Discharge
https://www.maplesoft.com/applications/view.aspx?SID=154645&ref=Feed
Consider a long rectangular concrete channel that ends in an abrupt freefall, with an inflow of water along its length.
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This application will calculate the profile of the water surface from the freefall to a specified distance upstream by numerically solving the governing differential equation.
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For a subcritical flow, downstream conditions determine the water surface profile. The water depth reaches the critical height (i.e. the minimum energy height) at a short distance before the freefall - this is the boundary condition on the solution of the governing differential equation.<img src="https://www.maplesoft.com/view.aspx?si=154645/Spatially_Varied_Open-Channel_Flow_with_Increasing_Discharge.png" alt="Spatially Varied Open-Channel Flow with Increasing Discharge" style="max-width: 25%;" align="left"/>Consider a long rectangular concrete channel that ends in an abrupt freefall, with an inflow of water along its length.
<BR><BR>
This application will calculate the profile of the water surface from the freefall to a specified distance upstream by numerically solving the governing differential equation.
<BR><BR>
For a subcritical flow, downstream conditions determine the water surface profile. The water depth reaches the critical height (i.e. the minimum energy height) at a short distance before the freefall - this is the boundary condition on the solution of the governing differential equation.https://www.maplesoft.com/applications/view.aspx?SID=154645&ref=FeedMon, 25 May 2020 04:00:00 ZSamir KhanSamir KhanGradually Varied Flow in a Trapezoidal Channel
https://www.maplesoft.com/applications/view.aspx?SID=154642&ref=Feed
Water flows along a gently sloped trapezoidal channel; this is known as gradually varied flow.
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As the flow progresses along the channel, the water depth eventually reaches a uniform depth that no longer changes with distance along the channel; this is known as the normal depth.
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This application derives a fully analytical differential equation for gradually varied flow in a trapezoidal channel. The differential equation is solved numerically, and the resulting water surface profile is plotted.<img src="https://www.maplesoft.com/view.aspx?si=154642/Trapezoidal_Channel.png" alt="Gradually Varied Flow in a Trapezoidal Channel" style="max-width: 25%;" align="left"/>Water flows along a gently sloped trapezoidal channel; this is known as gradually varied flow.
<BR><BR>
As the flow progresses along the channel, the water depth eventually reaches a uniform depth that no longer changes with distance along the channel; this is known as the normal depth.
<BR><BR>
This application derives a fully analytical differential equation for gradually varied flow in a trapezoidal channel. The differential equation is solved numerically, and the resulting water surface profile is plotted.https://www.maplesoft.com/applications/view.aspx?SID=154642&ref=FeedThu, 21 May 2020 04:00:00 ZSamir KhanSamir KhanSpeed of Sound in Various Fluids
https://www.maplesoft.com/applications/view.aspx?SID=154641&ref=Feed
This application computes and tabulates the speed of sound in various fluids at standard temperature and pressure, as provided by the ThermophysicalData package (which uses the open-source CoolProp project for fluid properties).
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The list of fluids include water, ethanol, air, ammonia and several others. However, you can use any of the fluids in the ThermophysicalData package (this help page contains a list of available fluids).
<BR><BR>
This application also demonstrates the use of the DocumentTools package for tabulating and formatting results.<img src="https://www.maplesoft.com/view.aspx?si=154641/thumb.png" alt="Speed of Sound in Various Fluids" style="max-width: 25%;" align="left"/>This application computes and tabulates the speed of sound in various fluids at standard temperature and pressure, as provided by the ThermophysicalData package (which uses the open-source CoolProp project for fluid properties).
<BR><BR>
The list of fluids include water, ethanol, air, ammonia and several others. However, you can use any of the fluids in the ThermophysicalData package (this help page contains a list of available fluids).
<BR><BR>
This application also demonstrates the use of the DocumentTools package for tabulating and formatting results.https://www.maplesoft.com/applications/view.aspx?SID=154641&ref=FeedFri, 08 May 2020 04:00:00 ZSamir KhanSamir KhanShifting the Pitch of Audio in the Frequency Domain
https://www.maplesoft.com/applications/view.aspx?SID=154638&ref=Feed
This application will shift the pitch of an audio file by scaling its frequency spectrum.
<BR><BR>
Our simple approach will multiply each signal frequency by the same amount. For a piano or violin note, the harmonics will still be an integer multiple of the pitch with the same balance between amplitudes (baring some digital aliasing effects). This preserves the timbre of the sound.
<BR><BR>
If your original audio is a piano note at F4 (a pitch of 349.2 Hz), you can convert it to an A4 note by scaling the frequencies by 4 semitones (a pitch of 349.2 Hz 4/12 = 440.0 Hz).<img src="https://www.maplesoft.com/view.aspx?si=154638/Pitch_Shift.png" alt="Shifting the Pitch of Audio in the Frequency Domain" style="max-width: 25%;" align="left"/>This application will shift the pitch of an audio file by scaling its frequency spectrum.
<BR><BR>
Our simple approach will multiply each signal frequency by the same amount. For a piano or violin note, the harmonics will still be an integer multiple of the pitch with the same balance between amplitudes (baring some digital aliasing effects). This preserves the timbre of the sound.
<BR><BR>
If your original audio is a piano note at F4 (a pitch of 349.2 Hz), you can convert it to an A4 note by scaling the frequencies by 4 semitones (a pitch of 349.2 Hz 4/12 = 440.0 Hz).https://www.maplesoft.com/applications/view.aspx?SID=154638&ref=FeedMon, 04 May 2020 04:00:00 ZSamir KhanSamir KhanPressure Drop of Gas and Liquid Flowing in a Pipe
https://www.maplesoft.com/applications/view.aspx?SID=154636&ref=Feed
This application calculates the two-phase pressure gradient for gas and liquid flowing in a pipe. The Lockhart-Martinelli separated flow approach is used.<img src="https://www.maplesoft.com/view.aspx?si=154636/pipe.png" alt="Pressure Drop of Gas and Liquid Flowing in a Pipe" style="max-width: 25%;" align="left"/>This application calculates the two-phase pressure gradient for gas and liquid flowing in a pipe. The Lockhart-Martinelli separated flow approach is used.https://www.maplesoft.com/applications/view.aspx?SID=154636&ref=FeedMon, 20 Apr 2020 04:00:00 ZSamir KhanSamir KhanBraking Distance of a Skidding Car
https://www.maplesoft.com/applications/view.aspx?SID=154632&ref=Feed
You're driving a car on an incline, but the brakes lock up. How far will your car skid?
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This application uses Newton's 2nd law and laws of motion to derive an equation that gives the distance your car will skid (also known as the braking distance). This equation shows that the braking distance is proportional to the square of the velocity at the start of the skid.<img src="https://www.maplesoft.com/view.aspx?si=154632/Braking_Distance_of_a_Skidding_Car.png" alt="Braking Distance of a Skidding Car" style="max-width: 25%;" align="left"/>You're driving a car on an incline, but the brakes lock up. How far will your car skid?
<BR><BR>
This application uses Newton's 2nd law and laws of motion to derive an equation that gives the distance your car will skid (also known as the braking distance). This equation shows that the braking distance is proportional to the square of the velocity at the start of the skid.https://www.maplesoft.com/applications/view.aspx?SID=154632&ref=FeedFri, 17 Apr 2020 04:00:00 ZSamir KhanSamir KhanHow Cold Can a Zeer Pot Get?
https://www.maplesoft.com/applications/view.aspx?SID=154633&ref=Feed
A Zeer pot is an evaporative cooler made of two clay or terracotta pots. One is placed inside the other and the gap filled with wet sand, and a wet cloth is placed on top. Vegetables or fruit are usually placed in the inner pot. As the water from the sand evaporates, the inner pot is cooled. Water wicks throughout the sand to maintain a consistent temperature throughout.
<BR><BR>
The coldest possible temperature that can be achieved is the wet-bulb temperature, and can be computed with Maple's ThermophysicalData package. The wet bulb temperature is a function of the relative humidity (i.e. the water content) and temperature of the ambient air.
<BR><BR>
This application plots the coldest possible temperature in a Zeer pot for a range of relative humidities.<img src="https://www.maplesoft.com/view.aspx?si=154633/ZeerPot.png" alt="How Cold Can a Zeer Pot Get?" style="max-width: 25%;" align="left"/>A Zeer pot is an evaporative cooler made of two clay or terracotta pots. One is placed inside the other and the gap filled with wet sand, and a wet cloth is placed on top. Vegetables or fruit are usually placed in the inner pot. As the water from the sand evaporates, the inner pot is cooled. Water wicks throughout the sand to maintain a consistent temperature throughout.
<BR><BR>
The coldest possible temperature that can be achieved is the wet-bulb temperature, and can be computed with Maple's ThermophysicalData package. The wet bulb temperature is a function of the relative humidity (i.e. the water content) and temperature of the ambient air.
<BR><BR>
This application plots the coldest possible temperature in a Zeer pot for a range of relative humidities.https://www.maplesoft.com/applications/view.aspx?SID=154633&ref=FeedFri, 17 Apr 2020 04:00:00 ZSamir KhanSamir KhanExtract the Envelope and Instantaneous Phase of a Signal using the Hilbert Transform
https://www.maplesoft.com/applications/view.aspx?SID=154634&ref=Feed
The Hilbert transform has many practical applications. These include vibration analysis and amplitude modulation in communication systems
<BR><BR>
This application compute the envelope and instantaneous frequency of a signal using the Hilbert transform.
<UL>
<LI>The signal envelope is the magnitude of the Hilbert transform
<LI>The instantaneous frequency is the derivative (wrt time) of the phase angle of the Hilbert transform (only for single-component signals)
</UL>
The magnitude of the analytic signal captures the slowly varying features of the signal, while the phase contains the high-frequency information.<img src="https://www.maplesoft.com/view.aspx?si=154634/Hilbert_Transform.png" alt="Extract the Envelope and Instantaneous Phase of a Signal using the Hilbert Transform" style="max-width: 25%;" align="left"/>The Hilbert transform has many practical applications. These include vibration analysis and amplitude modulation in communication systems
<BR><BR>
This application compute the envelope and instantaneous frequency of a signal using the Hilbert transform.
<UL>
<LI>The signal envelope is the magnitude of the Hilbert transform
<LI>The instantaneous frequency is the derivative (wrt time) of the phase angle of the Hilbert transform (only for single-component signals)
</UL>
The magnitude of the analytic signal captures the slowly varying features of the signal, while the phase contains the high-frequency information.https://www.maplesoft.com/applications/view.aspx?SID=154634&ref=FeedFri, 17 Apr 2020 04:00:00 ZSamir KhanSamir KhanThe Color of Noise
https://www.maplesoft.com/applications/view.aspx?SID=154635&ref=Feed
You've probably heard the sound of white noise. It's what we perceive as a hiss, and has a flat spectral content across all frequencies. But many other colors of noise exist, each with a different spectral "slope". Some emphasize lower frequencies, while others have a U-shape spectral weighting.
<BR><BR>
Common noise colors include pink, red, blue and violet, each with different properties and applications.
<UL>
<LI>Pink noise, for example, better represents natural phenomena like rain and has been shown to aid sleep and memory
<LI>Blue noise is used in audio dithering to mask the effect of quantization
</UL>
This application generates 1D pink, red, blue and violet noise, and produces periodograms for each. Each noise sample is sonified so you can hear what it sounds like.
<BR><BR>
Additionally, the sound can also be exported to a wave file for use in another tool (Maple will export high precision 32-bit and 64-bit wave files).<img src="https://www.maplesoft.com/view.aspx?si=154635/pinkNoise.png" alt="The Color of Noise" style="max-width: 25%;" align="left"/>You've probably heard the sound of white noise. It's what we perceive as a hiss, and has a flat spectral content across all frequencies. But many other colors of noise exist, each with a different spectral "slope". Some emphasize lower frequencies, while others have a U-shape spectral weighting.
<BR><BR>
Common noise colors include pink, red, blue and violet, each with different properties and applications.
<UL>
<LI>Pink noise, for example, better represents natural phenomena like rain and has been shown to aid sleep and memory
<LI>Blue noise is used in audio dithering to mask the effect of quantization
</UL>
This application generates 1D pink, red, blue and violet noise, and produces periodograms for each. Each noise sample is sonified so you can hear what it sounds like.
<BR><BR>
Additionally, the sound can also be exported to a wave file for use in another tool (Maple will export high precision 32-bit and 64-bit wave files).https://www.maplesoft.com/applications/view.aspx?SID=154635&ref=FeedFri, 17 Apr 2020 04:00:00 ZSamir KhanSamir KhanGenerate the Sound of Plucked Instruments with the Karplus-Strong Algorithm
https://www.maplesoft.com/applications/view.aspx?SID=154630&ref=Feed
This application implements the Karplus-Strong string synthesis method to generate the sound of a plucked instrument.
<BR><BR>
Despite its simplicity, this algorithm can create remarkably realistic sounds. You can even extend the application to generate the sound of strummed chords.
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As a further step (not shown here), you add special effects like reverb and echo by convolving the generated sound with an impulse response.<img src="https://www.maplesoft.com/view.aspx?si=154630/KarplusStrong.png" alt="Generate the Sound of Plucked Instruments with the Karplus-Strong Algorithm" style="max-width: 25%;" align="left"/>This application implements the Karplus-Strong string synthesis method to generate the sound of a plucked instrument.
<BR><BR>
Despite its simplicity, this algorithm can create remarkably realistic sounds. You can even extend the application to generate the sound of strummed chords.
<BR><BR>
As a further step (not shown here), you add special effects like reverb and echo by convolving the generated sound with an impulse response.https://www.maplesoft.com/applications/view.aspx?SID=154630&ref=FeedTue, 07 Apr 2020 04:00:00 ZSamir KhanSamir KhanCalculate Order of Butterworth Filter for User-Defined Design Requirements
https://www.maplesoft.com/applications/view.aspx?SID=154629&ref=Feed
This worksheet will help you calculate the order of a lowpass Butterworth filter with a user-defined minimum gain at a user-defined frequency. Additionally, once the order is known, the filter gain is plotted.<img src="https://www.maplesoft.com/view.aspx?si=154629/thumb.png" alt="Calculate Order of Butterworth Filter for User-Defined Design Requirements" style="max-width: 25%;" align="left"/>This worksheet will help you calculate the order of a lowpass Butterworth filter with a user-defined minimum gain at a user-defined frequency. Additionally, once the order is known, the filter gain is plotted.https://www.maplesoft.com/applications/view.aspx?SID=154629&ref=FeedFri, 03 Apr 2020 04:00:00 ZSamir KhanSamir KhanDouble Stub Matching
https://www.maplesoft.com/applications/view.aspx?SID=154628&ref=Feed
This application will calculate the lengths of two shunt stubs that match the load to the impedance of a transmission line.<img src="https://www.maplesoft.com/view.aspx?si=154628/double_stub.png" alt="Double Stub Matching" style="max-width: 25%;" align="left"/>This application will calculate the lengths of two shunt stubs that match the load to the impedance of a transmission line.https://www.maplesoft.com/applications/view.aspx?SID=154628&ref=FeedThu, 02 Apr 2020 04:00:00 ZSamir KhanSamir Khan