% ECE 1250 S12 Lecture M9

% Today's lecture focuses on signal processing.  See separate figure "Filtering" %  showing a comparison of filtering of continuous-time signals versus 
%  discrete-time signals.

% The key message for our class from the filtering discussion is that we can
%  use the Fast Fourier Transform (fft) to find the spectrum of a signal, and
%  the spectrum tells us what frequencies are present in a signal.  It is
%  equivalent to a set of phasors for frequencies (equally spaced) from DC to
%  the sampling rate of the signal.  The idea is that the signal is equivalent
%  to a summation of sinusoids, and the spectrum tells us what those sinusoids
%  are.

% If we want to modify a signal, we can modify its spectrum.  This has the 
%  advantage that we intuitively understand how changing the frequency content
%  of a sound will affect it.  We are familiar with bass and treble controls
%  that alter the amount of low or high frequency content of a signal.

% To get back to the time domain after altering the spectrum, we can use an
%  inverse fft (ifft function in Matlab).

% Two examples of altering the spectrum are the following script files:
% 1) real_fft.m   We zero out the imaginary part of the spectrum.  This is
%                 equivalent to changing the phase shift of the sinusoids
%                 in a signal.  It creates a strange reverberation as though
%                 the singers are getting ahead of themselves.
%
% 2) chop_spec.m  We zero out reqularly spaced bands of frequencies in the
%                 spectrum.  The result is a mechanical sounding music clip
%                 in which mostly the "ah" sounds come through.

% Filtering a signal means letting certain frequencies through and not others.
% butter_filter.m
%--------------------------------------------------------------------------------