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Spectrogram Examples-2 • • • • • • • • • • • • • • • • • • •
%spcgrm; x=logon(50,0.3,200)+logon(130,0.7,200)+logon(140,-0.5,200); S1=specgram(x,256,200,16,15); S2=specgram(x,256,200,32,31); S3=specgram(x,256,200,64,63); S4=specgram(x,256,200,128,127); subplot(221); imagesc(abs(S1)); subplot(222); imagesc(abs(S2)); subplot(223); imagesc(abs(S3)); subplot(224); imagesc(abs(S4)); %example 2; x=exp(j*0.5*[1:200])+exp(j*2*[1:200]); S=specgram(x,256,200,32,31); figure imagesc(abs(S));
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MATLAB code • • • • • • • • • • • • • • • • • • • • •
You can use the MATLAB command: specgram SPECGRAM Spectrogram using a Short-Time Fourier Transform (STFT). B = SPECGRAM(A) calculates the spectrogram for the signal in vector A. SPECGRAM divides the signal into overlapping segments, windows each segment and forms the columns of B with their discrete Fourier transforms. B = SPECGRAM(A,NFFT,Fs) specifies the number of FFT points used to calculate the discrete Fourier transforms. If NFFT = [] or is not specified the default NFFT = minimum of 256 and the length of A. Fs is the sampling frequency which does not effect the spectrogram but is used for scaling plots. If Fs=[] or is not specified it defaults to 2 Hz. B = SPECGRAM(A,NFFT,Fs,WINDOW,NOVERLAP) uses WINDOW to window each overlapping segment and forms the columns of B with their zero-padded, length NFFT discrete Fourier transforms. If you specify a scalar for WINDOW, SPECGRAM uses a Hanning window of length NFFT. WINDOW must have a length smaller than or equal to NFFT and greater than NOVERLAP. NOVERLAP is the number of samples each segement of A overlaps. The default value of NOVERLAP = length(WINDOW)/2.
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Example • • • • • • • • • • • • • • • • • • • • • • • • • • •
%logon; x=logon(64,0.4,128); tflog=specgram(x,32,128,32,31); subplot(211); plot(real(x)); subplot(212); imagesc(abs(tflog)); pause; figure %demo signal; tfdemo=specgram(demosig,32,200,32,31); imagesc(abs(tfdemo)); pause figure; % effect of the window length; y=[zeros(1,128),exp(j*0.6*[1:128])]; subplot(411); plot(real(y)); subplot(412); tf1=specgram(y,16,256,16,15); imagesc(abs(tf1)); subplot(413); tf2=specgram(y,32,256,32,31); imagesc(abs(tf2)); subplot(414); tf3=specgram(y,64,256,64,63); imagesc(abs(tf3));
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t=0:0.001:2; % 2 secs @ 1kHz sample rate tf1=specgram(y,256,1E3,256,250); y=chirp(t,0,1,150); % Start @ DC, cross 150Hz at t=1sec t=-2:0.001:2; % +/-2 secs @ 1kHz sample rate y=chirp(t,100,1,200,'q'); % Start @ 100Hz, cross 200Hz at t=1sec tf2=specgram(y,128,1E3,128,120); % Display the spectrogram figure; subplot(211) imagesc(abs(tf1)); title('Linear Chirp: start at DC, cross 150Hz at t=1sec'); subplot(212) imagesc(abs(tf2)); title('Quadractic Chip: start at 100Hz and cross 200Hz at t=1sec');
Chirp Signals Linear Chirp: start at DC, cross 150Hz at t=1sec 20 40 60 80 100 120 50
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Quadractic Chip: start at 100Hz and cross 200Hz at t=1sec
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Spectrogram Examples-2 • • • • • • • • • • • • • • • • • • •
%spcgrm; x=logon(50,0.3,200)+logon(130,0.7,200)+logon(140,-0.5,200); S1=specgram(x,256,200,16,15); S2=specgram(x,256,200,32,31); S3=specgram(x,256,200,64,63); S4=specgram(x,256,200,128,127); subplot(221); imagesc(abs(S1)); subplot(222); imagesc(abs(S2)); subplot(223); imagesc(abs(S3)); subplot(224); imagesc(abs(S4)); %example 2; x=exp(j*0.5*[1:200])+exp(j*2*[1:200]); S=specgram(x,256,200,32,31); figure imagesc(abs(S));
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MATLAB code • • • • • • • • • • • • • • • • • • • • •
You can use the MATLAB command: specgram SPECGRAM Spectrogram using a Short-Time Fourier Transform (STFT). B = SPECGRAM(A) calculates the spectrogram for the signal in vector A. SPECGRAM divides the signal into overlapping segments, windows each segment and forms the columns of B with their discrete Fourier transforms. B = SPECGRAM(A,NFFT,Fs) specifies the number of FFT points used to calculate the discrete Fourier transforms. If NFFT = [] or is not specified the default NFFT = minimum of 256 and the length of A. Fs is the sampling frequency which does not effect the spectrogram but is used for scaling plots. If Fs=[] or is not specified it defaults to 2 Hz. B = SPECGRAM(A,NFFT,Fs,WINDOW,NOVERLAP) uses WINDOW to window each overlapping segment and forms the columns of B with their zero-padded, length NFFT discrete Fourier transforms. If you specify a scalar for WINDOW, SPECGRAM uses a Hanning window of length NFFT. WINDOW must have a length smaller than or equal to NFFT and greater than NOVERLAP. NOVERLAP is the number of samples each segement of A overlaps. The default value of NOVERLAP = length(WINDOW)/2.
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Example • • • • • • • • • • • • • • • • • • • • • • • • • • •
%logon; x=logon(64,0.4,128); tflog=specgram(x,32,128,32,31); subplot(211); plot(real(x)); subplot(212); imagesc(abs(tflog)); pause; figure %demo signal; tfdemo=specgram(demosig,32,200,32,31); imagesc(abs(tfdemo)); pause figure; % effect of the window length; y=[zeros(1,128),exp(j*0.6*[1:128])]; subplot(411); plot(real(y)); subplot(412); tf1=specgram(y,16,256,16,15); imagesc(abs(tf1)); subplot(413); tf2=specgram(y,32,256,32,31); imagesc(abs(tf2)); subplot(414); tf3=specgram(y,64,256,64,63); imagesc(abs(tf3));
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t=0:0.001:2; % 2 secs @ 1kHz sample rate tf1=specgram(y,256,1E3,256,250); y=chirp(t,0,1,150); % Start @ DC, cross 150Hz at t=1sec t=-2:0.001:2; % +/-2 secs @ 1kHz sample rate y=chirp(t,100,1,200,'q'); % Start @ 100Hz, cross 200Hz at t=1sec tf2=specgram(y,128,1E3,128,120); % Display the spectrogram figure; subplot(211) imagesc(abs(tf1)); title('Linear Chirp: start at DC, cross 150Hz at t=1sec'); subplot(212) imagesc(abs(tf2)); title('Quadractic Chip: start at 100Hz and cross 200Hz at t=1sec');
Chirp Signals Linear Chirp: start at DC, cross 150Hz at t=1sec 20 40 60 80 100 120 50
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Quadractic Chip: start at 100Hz and cross 200Hz at t=1sec
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