How can I plot spectrogram without using function "spectrogram"?

SPECTROGRAM Spectrogram using a Short-Time Fourier Transform (STFT). S = SPECTROGRAM(X) returns the short-time Fourier transform of the signal specified by vector X in the matrix S. By default, X is divided into eight segments with 50% overlap, and each segment is windowed with a Hamming window. The number of frequency points used to calculate the discrete Fourier transforms is equal to the larger of 256 or the next power of two greater than the segment length. If X cannot be divided exactly into eight segments, X will be truncated. S = SPECTROGRAM(X,WINDOW), when WINDOW is a vector, divides X into segments of the same length as WINDOW, and then windows each segment with the vector specified in WINDOW. If WINDOW is an integer, the function divides X into segments of length equal to that integer value and windows each segment with a Hamming window. If WINDOW is not specified, the default is used. S = SPECTROGRAM(X,WINDOW,NOVERLAP) specifies NOVERLAP samples of overlap between adjoining segments. NOVERLAP must be an integer smaller than WINDOW if WINDOW is an integer. NOVERLAP must be an integer smaller than the length of WINDOW if WINDOW is a vector. If NOVERLAP is not specified, the default value is used to obtain a 50% overlap. S = SPECTROGRAM(X,WINDOW,NOVERLAP,NFFT) specifies the number of frequency points used to calculate the discrete Fourier transforms. If NFFT is not specified, the default NFFT is used. S = SPECTROGRAM(X,WINDOW,NOVERLAP,NFFT,Fs) specifies the sample rate, Fs, in Hz. If Fs is specified as empty, it defaults to 1 Hz. If it is not specified, normalized frequency is used. Each column of S contains an estimate of the short-term, time-localized frequency content of X. Time increases across the columns of S, from left to right. Frequency increases down the rows, starting at 0. If X is a length NX complex signal, S is a complex matrix with NFFT rows and k = fix((NX-NOVERLAP)/(length(WINDOW)-NOVERLAP)) columns. For real X, S has (NFFT/2+1) rows if NFFT is even and (NFFT+1)/2 rows if NFFT is odd. [S,F,T] = SPECTROGRAM(...) returns a vector of frequencies, F, and a vector of times, T, at which the spectrogram is computed. F has length equal to the number of rows of S. T has length k (defined above) and its value corresponds to the center of each segment. If a sample rate is not provided, F contains normalized frequencies. [S,F,T] = SPECTROGRAM(X,WINDOW,NOVERLAP,F) computes the two-sided spectrogram at the normalized frequencies specified in the vector F. F must have at least two elements. [S,F,T] = SPECTROGRAM(X,WINDOW,NOVERLAP,F,Fs) computes the two-sided spectrogram at the frequencies specified in vector F. F must be expressed in Hz and have at least two elements. [S,F,T,P] = SPECTROGRAM(...) P is a matrix representing the Power Spectral Density (PSD) of each segment. For real signals, SPECTROGRAM returns the one-sided modified periodogram estimate of the PSD of each segment; for complex signals and in the case when a vector of frequencies is specified, it returns the two-sided PSD. [S,F,T,P] = SPECTROGRAM(...,'MinThreshold',THRESH) sets the elements of P to zero when the corresponding elements of 10*log10(P) are less than THRESH. Specify THRESH in decibels. The default value of THRESH is -Inf. [S,F,T,P] = SPECTROGRAM(...,'reassigned') reassigns each PSD estimate to the location of its center of gravity. The reassignment is done in-place and returned in P. [S,F,T,P,Fc,Tc] = SPECTROGRAM(...) returns the locations in frequency and time of the center of gravity of each estimate in the spectrogram. The frequencies and times are returned in matrices, Fc, and Tc, respectively. Fc and Tc have the same dimensions as the spectrogram, S. [...] = SPECTROGRAM(...,SPECTRUMTYPE) uses the window scaling algorithm specified by SPECTRUMTYPE when computing the power spectral density matrix P. SPECTRUMTYPE can be set to 'psd' or 'power': 'psd' - returns the power spectral density. 'power' - scales each estimate of the PSD by the equivalent noise bandwidth of the window (in Hz). Use this option to obtain an estimate of the power at each frequency. The default value for SPECTRUMTYPE is 'psd'. [...] = SPECTROGRAM(...,FREQRANGE) returns the PSD over the specified range of frequencies based upon the value of FREQRANGE: 'onesided' - returns the one-sided matrix P of a real input signal X. If NFFT is even, P has NFFT/2+1 rows and is computed over the interval [0,pi]. If NFFT is odd, then P has (NFFT+1)/2 rows and is computed over the interval [0,pi). When Fs is specified, the intervals become [0,Fs/2] and [0,Fs/2) for even and odd NFFT, respectively. 'twosided' - returns the two-sided matrix P for either real or complex input X. P has NFFT rows and is computed over the interval [0,2*pi). When Fs is specified, the interval becomes [0,Fs). 'centered' - returns the centered two-sided matrix P for either real or complex X. P has NFFT rows and is computed over the interval (-pi,pi] for even length NFFT and (-pi,pi) for odd length NFFT. When Fs is specified, the intervals become (-Fs/2, Fs/2] and (-Fs/2,Fs/2) for even and odd NFFT, respectively. FREQRANGE may be placed in any position in the input argument list after NOVERLAP. The default value of FREQRANGE is 'onesided' when X is real and 'twosided' when X is complex. [...] = SPECTROGRAM(...,'OutputTimeDimension',TIMEDIMENSION) specifies the orientation of S, T, P, Fc, and Tc according to the location of the time dimension. If TIMEDIMENSION is set to 'downrows', the time dimension of S, P, Fc, and Tc is down the rows and the frequency dimension is across the columns. T is returned as a column vector. If TIMEDIMENSION is set to 'acrosscolumns', the time dimension of S, P, Fc, and Tc is across the columns and the frequency dimension is down the rows. T is returned as a row vector. This argument is ignored if this function is called with no output arguments. The default value is 'acrosscolumns'. SPECTROGRAM(...) with no output arguments plots the PSD estimate for each segment on a surface in the current figure. SPECTROGRAM(...,FREQLOCATION) controls where MATLAB displays the frequency axis on the plot. This string can be either 'xaxis' or 'yaxis'. Setting this FREQLOCATION to 'yaxis' displays frequency on the y-axis and time on the x-axis. The default is 'xaxis' which displays the frequency on the x-axis. If FREQLOCATION is specified when output arguments are requested, it is ignored. EXAMPLE 1: Spectrogram of quadratic chirp t=0:0.001:2; % 2 secs @ 1kHz sample rate y=chirp(t,100,1,200,'q'); % Start @ 100Hz, cross 200Hz at t=1sec spectrogram(y,kaiser(128,18),120,128,1E3,'yaxis'); title('Quadratic Chirp: start at 100Hz and cross 200Hz at t=1sec'); EXAMPLE 2: Reassigned spectrogram of quadratic chirp t=0:0.001:2; % 2 secs @ 1kHz sample rate y=chirp(t,100,1,200,'q'); % Start @ 100Hz, cross 200Hz at t=1sec spectrogram(y,kaiser(128,18),120,128,1E3,'reassigned','yaxis'); title('Quadratic Chirp: start at 100Hz and cross 200Hz at t=1sec'); EXAMPLE 3: Plot instantaneous frequency of quadratic chirp t=0:0.001:2; % 2 secs @ 1kHz sample rate y=chirp(t,100,1,200,'q'); % Start @ 100Hz, cross 200Hz at t=1sec % remove estimates less than -30 dB [~,~,~,P,Fc,Tc] = spectrogram(y,kaiser(128,18),120,128,1E3,'minthreshold',-30); plot(Tc(P>0),Fc(P>0),'. ') title('Quadratic Chirp: start at 100Hz and cross 200Hz at t=1sec'); xlabel('Time (s)') ylabel('Frequency (Hz)') EXAMPLE 4: Waterfall display of the PSD of each segment of a VCO Fs = 10e3; t = 0:1/Fs:2; x1 = vco(sawtooth(2*pi*t,0.5),[0.1 0.4]*Fs,Fs); spectrogram(x1,kaiser(256,5),220,512,Fs); view(-45,65) colormap bone See also PERIODOGRAM, PWELCH, GOERTZEL. Documentation for spectrogram doc spectrogram Other uses of spectrogram gpuArray/spectrogram tall/spectrogram