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Spectrogram Analysis and Applications
Overview
The frequency characteristics of nonstationary signals vary as a function of time. This requires Fourier
analysis of these signals to be localized and time-dependent, resulting in analysis methods known as time-
frequency distributions. One elementary time-frequency distribution based on the FFT is the short-time
Fourier Transform (STFT). The STFT applied to speech is often called a
speech spectrogram
.
Spectrograms are well suited to analyze speech signals with their time-varying narrowband features.
In this project, you will:
•
Calculate spectrogra ms of frequency modulated signals.
•
Construct n arrowband and wideband sp ectrogra ms of sp e ech signals.
•
Estimat e a sp e ech signal from a m odified STFT.
•
Modify the time scale of a spe ech signal.
The project zip file contains the audio files and MATLAB functions which you will ne ed for this proje
To access the zip file, click on the link b elow where you found this file on the web site.
Spectrogram Definition
The sp ectrogra m of a signal
x[n]
is d efined a s:
where
ϖ
[n]
is the window used. The window will determine what portion of the signal is used for
a n alysis and controls the frequency resolution of the spectrogra m. The para m et er
n
d enotes the reference
position of the window on the signal. Let the window be of length
N
win
and nonzero only in the interval
0
≤ k ≤ (N
win
- 1)
. The above equation reduces to:
f200b

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*Sign up* Computing Spectrograms in MATLAB
It is easy to construct spectrograms in M
ATLAB
since the STFT involves only windowing and the FFT.
This project will require extensive use of the M
ATLAB
function
spectrogram
. It is suggested you take
some time to fully understand the details of the
spectrogram
function. This can be done by typing
help
spectrogram
at the M
ATLAB
prompt. For a more graphical presentation of the help (including figures) try
doc spectrogram
. A few important points about the
spectrogram
function for this project:
•
Note that if the spectrogram is defined as it is in the previous section, the first column of
the spectrogram generated by
MATLAB
is really , not
X
0
(
ϖ
)
.
•
The
spectrogram
function with no output arguments will plot the results to the current
figure.
•
For real signals
x[n]
, the
spectrogram
function only calculates or plots a portion of the
frequency components (from 0 to
π
) since the remaining are “redundant”. How are they
“redundant”?
•
It is common in speech processing to use a “short” time window and to plot frequency on
the y axis. When you have loaded the speech signals mentioned below, the command
spectrogram(s1,hamming(256),’yaxis’)
will produce a good example
spectrogram plot. Please use the ‘yaxis’ parameter for all your figures.
The MATLAB function

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