Matlab

MATLAB for Audio Signal
Processing
P. Professorson
UT Arlington Night School

MATLAB for Audio Signal
Processing
●

Getting real world data into your computer

●

Analysis based on frequency content
–

●

Fourier analysis

Modifying the spectrum
–

Filtering signal bands
●
●

●

FIR filters
IIR filters

Other stuff

Getting data into the computer
MicrophoneAnti-Aliasing
filter

Continuous

Sample &
Hold

Analog to
Digital
converter

DSP
system

Discrete
(fixed bits per sample)

Analog

Digital

Aliasing
●

Sampling frequency must be high enough to
characterize the signal correctly.
–

●

Fs >= 2 fmax

For a given Fs, signal components higher
than Fs/2 (Nyquist frequency) are forcibly
removed using ananti-aliasing filter prior to
sampling.

Blue signal : 5 Hz
Red signal : 30 Hz
Sampling frequency : 80 Hz
Nyquist frequency : 40 Hz
No aliasing in either signal.

Sampling frequency : 40 Hz
No aliasing in blue signal.
Nyquist frequency : 20 Hz
Aliasing in red signal. The 30
Hz signal manifests itself as a
10 Hz signal in the sampled
system.

Audio signals
●

Audio spectrum for music liesbetween 20Hz
to 20KHz

●

This gives a Nyquist sampling rate of 40KHz

●

CD audio uses a sampling rate of 44.1 KHz

●

16 bits per sample

●

WAV files store uncompressed samples

●

MP3 files store compressed data

Importing audio in MATLAB
●

WAV files:
–
–

sr: sampling rate

–

nbits: number of bits per sample

–

For mono audio, data is a vectorcontaining
audio samples

–
●

[data sr nbits] = wavread('song.wav');

For stereo audio, data is a 2-D vector

MP3 files – convert them to WAV format using
an external MP3 decoder, then use wavread

Playing back your audio
●

Create an audioplayer object
–

●

ap = audioplayer(data, sr);

Play the audio file using the object just
created
–

play(ap);
●

●

–

Thisplays the audio in the background while
the rest of your scrip continues working.
isplaying(ap) returns 1 if the file is still playing,
and 0 if the file has finished playback.

playblocking(ap);
●

This halts execution till the audio clip stops
playing

Audio spectrum
●

Human ear's response is non-linear. It is good
at discriminating low frequencies, but not so
good atdistinguishing between higher
frequencies.

●

Spectrum analyzers on music players have
logarithmic frequency scales.

●

Octave is a frequency scale that doubles at
every level.
–

F1 = 30Hz, F2 = 60Hz, F3 = 120Hz …

Discrete-time Fourier Analysis
●

Discrete Fourier Transform gives a discretefrequency representation of a discrete time
signal.

●

An N-point DFT of a signal willproduce N
numbers, each representing the signal
content at uniformly spaced frequencies
between - Fs/2 to + Fs/2 (not in that order).

●

Fast Fourier Transform (FFT) is a (class of)
algorithm(s) that produce the DFT efficiently
- O(N*log(N)) vs O(N2) for regular DFT.

MATLAB's FFT
●

f = fft(signal, N);
–

Produces N-point DFT of a signal

–

N should be > length of signal topreserve
fidelity, preferably a power of 2 for efficiency

●

For a real signal, f is generally complex. Its
absolute value is used to specify its
strength.

●

signal2 = ifft(f, M)
–

Reproduces a signal of length M whose Npoint DFT is specified in f

FFT fun facts
●

f = fft(signal, N);
–

f(1) is the DC component / signal average
●

Useless with respect to audio spectrum–

f(2) is the strength at frequency Fs/N

–

f(k) is the strength at frequency (k-1)*Fs/N

–

f(N/2+1) is the strength at Nyquist frequency Fs/2
●

Useless as it varies with phase of the signal

–

–

f needs to be scaled as f*2/N

–

●

Beyond this are negative frequencies which are mirror
images of positive frequencies (for real signals)
FFT bins represent the...