Part 2 (based on Section 9.6.2): Short Time Fourier Transform (STFT) We illustrate the application of the STFT for analysis of a linear chirp signal whose frequency varies linearly over time: x(1) = cos(2π fol+wal²), 0 0, we have an "up-chirp" with increasing frequency, whereas for a <0, we have a "down-chirp" with decreasing frequency. (10) Use Matlab's chirp command to generate a 1 second linear chirp with starting frequency 200 Hz, ending frequency 600 Hz, sampled at 1500 Hz. Play the sound to verify to your satisfaction that you do hear an increasing pitch. (11) You have a chirp with about 1000 samples from (10), sampled at √ = 1.5 KHz. Plot the magnitude of the DTFT against frequency, using the canonical interval [-f/2, J./2]. (Estimate the DTFT using a "sufficiently long" DFT.) Discuss what you see in terms of frequency content. Can you tell that the signal is a chirp? (12) Now, compute an STFT using a length L = 32 Hann window, a length 512 FFT, and 25% overlap across successive windows. You may use Matlab's spectrogram command using the appropriate parameters. Display the magnitude of the STFT's frequency content versus time using Matlab's pcolor plot. The frequency axis should be in Hz and the time axis in seconds. Are you able to see the chirp frequency going from 100 to 400 Hz in 1 second? (13) Human speech is often analyzed using the STFT. Record 1 second of your own speech sampled at 8 KHz), and analyze it using a spectrogram. Use intervals of length 20 ms, a Hann window, a 50% overlap across successive windows, and an FFT size at least twice the number of samples. Plot the frequency content (as measured by STFT magnitude) versus time using pcolor. (14) Try recording drastically different speech segments and discuss whether you can "see" the differences in the STFT plots.
Part 2 (based on Section 9.6.2): Short Time Fourier Transform (STFT) We illustrate the application of the STFT for analysis of a linear chirp signal whose frequency varies linearly over time: x(1) = cos(2π fol+wal²), 0 0, we have an "up-chirp" with increasing frequency, whereas for a <0, we have a "down-chirp" with decreasing frequency. (10) Use Matlab's chirp command to generate a 1 second linear chirp with starting frequency 200 Hz, ending frequency 600 Hz, sampled at 1500 Hz. Play the sound to verify to your satisfaction that you do hear an increasing pitch. (11) You have a chirp with about 1000 samples from (10), sampled at √ = 1.5 KHz. Plot the magnitude of the DTFT against frequency, using the canonical interval [-f/2, J./2]. (Estimate the DTFT using a "sufficiently long" DFT.) Discuss what you see in terms of frequency content. Can you tell that the signal is a chirp? (12) Now, compute an STFT using a length L = 32 Hann window, a length 512 FFT, and 25% overlap across successive windows. You may use Matlab's spectrogram command using the appropriate parameters. Display the magnitude of the STFT's frequency content versus time using Matlab's pcolor plot. The frequency axis should be in Hz and the time axis in seconds. Are you able to see the chirp frequency going from 100 to 400 Hz in 1 second? (13) Human speech is often analyzed using the STFT. Record 1 second of your own speech sampled at 8 KHz), and analyze it using a spectrogram. Use intervals of length 20 ms, a Hann window, a 50% overlap across successive windows, and an FFT size at least twice the number of samples. Plot the frequency content (as measured by STFT magnitude) versus time using pcolor. (14) Try recording drastically different speech segments and discuss whether you can "see" the differences in the STFT plots.
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![Part 2 (based on Section 9.6.2): Short Time Fourier Transform (STFT)
We illustrate the application of the STFT for analysis of a linear chirp signal whose frequency
varies linearly over time:
x(1) = cos(2π fol+wal²), 0<t<Te
where the instantaneous frequency at time t€ [0,T] is given by differentiating the phase:
S(1)
1 d
2π dl
(2 fol+at²) = fo+at, 0<t<T
(3)
(4)
The instantaneous frequency varies from fo at time 0, to f₁ = Jo+aT at time T. The frequency
slope a has units of Hz per second: for a > 0, we have an "up-chirp" with increasing frequency,
whereas for a <0, we have a "down-chirp" with decreasing frequency.
(10) Use Matlab's chirp command to generate a 1 second linear chirp with starting frequency 200
Hz, ending frequency 600 Hz, sampled at 1500 Hz. Play the sound to verify to your satisfaction
that you do hear an increasing pitch.
(11) You have a chirp with about 1000 samples from (10), sampled at √ = 1.5 KHz. Plot the
magnitude of the DTFT against frequency, using the canonical interval [-f/2, J./2]. (Estimate
the DTFT using a "sufficiently long" DFT.) Discuss what you see in terms of frequency content.
Can you tell that the signal is a chirp?
(12) Now, compute an STFT using a length L = 32 Hann window, a length 512 FFT, and
25% overlap across successive windows. You may use Matlab's spectrogram command using the
appropriate parameters. Display the magnitude of the STFT's frequency content versus time
using Matlab's pcolor plot. The frequency axis should be in Hz and the time axis in seconds.
Are you able to see the chirp frequency going from 100 to 400 Hz in 1 second?
(13) Human speech is often analyzed using the STFT. Record 1 second of your own speech
sampled at 8 KHz), and analyze it using a spectrogram. Use intervals of length 20 ms, a Hann
window, a 50% overlap across successive windows, and an FFT size at least twice the number
of samples. Plot the frequency content (as measured by STFT magnitude) versus time using
pcolor.
(14) Try recording drastically different speech segments and discuss whether you can "see" the
differences in the STFT plots.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d86b7f3-5570-4ce2-ade5-b05f7393fda1%2F931b19a4-15f1-467e-8d5d-18b1c6177e85%2Fwf301m_processed.png&w=3840&q=75)
Transcribed Image Text:Part 2 (based on Section 9.6.2): Short Time Fourier Transform (STFT)
We illustrate the application of the STFT for analysis of a linear chirp signal whose frequency
varies linearly over time:
x(1) = cos(2π fol+wal²), 0<t<Te
where the instantaneous frequency at time t€ [0,T] is given by differentiating the phase:
S(1)
1 d
2π dl
(2 fol+at²) = fo+at, 0<t<T
(3)
(4)
The instantaneous frequency varies from fo at time 0, to f₁ = Jo+aT at time T. The frequency
slope a has units of Hz per second: for a > 0, we have an "up-chirp" with increasing frequency,
whereas for a <0, we have a "down-chirp" with decreasing frequency.
(10) Use Matlab's chirp command to generate a 1 second linear chirp with starting frequency 200
Hz, ending frequency 600 Hz, sampled at 1500 Hz. Play the sound to verify to your satisfaction
that you do hear an increasing pitch.
(11) You have a chirp with about 1000 samples from (10), sampled at √ = 1.5 KHz. Plot the
magnitude of the DTFT against frequency, using the canonical interval [-f/2, J./2]. (Estimate
the DTFT using a "sufficiently long" DFT.) Discuss what you see in terms of frequency content.
Can you tell that the signal is a chirp?
(12) Now, compute an STFT using a length L = 32 Hann window, a length 512 FFT, and
25% overlap across successive windows. You may use Matlab's spectrogram command using the
appropriate parameters. Display the magnitude of the STFT's frequency content versus time
using Matlab's pcolor plot. The frequency axis should be in Hz and the time axis in seconds.
Are you able to see the chirp frequency going from 100 to 400 Hz in 1 second?
(13) Human speech is often analyzed using the STFT. Record 1 second of your own speech
sampled at 8 KHz), and analyze it using a spectrogram. Use intervals of length 20 ms, a Hann
window, a 50% overlap across successive windows, and an FFT size at least twice the number
of samples. Plot the frequency content (as measured by STFT magnitude) versus time using
pcolor.
(14) Try recording drastically different speech segments and discuss whether you can "see" the
differences in the STFT plots.
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