Digital Signal Processing Reference
In-Depth Information
2. For each of the input frequencies given above, and using a sampling rate of 10 kHz, generate
and plot the ADC's sequence of output values. To do this, set up a time vector with one second's worth
of sampling times, and evaluate the values of a sine or cosine for the given input frequency, and plot the
result. Note: it is helpful to plot only about the first 50 samples of the output rather than the entire output.
3. State what value of cutoff frequency an anti-aliasing filter should have for the ADC of the above
exercises (i.e., an ADC operating at sampling rate of 10 kHz).
4. A certain system transmits any one of eight frequencies which are received at the input of an
ADC operating at 10 kHz. An anti-aliasing filter cutting off above 10 kHz (not 5 kHz, the Nyquist rate)
precedes the ADC. Using the folding diagram for 10 kHz, state the apparent frequency in the output
corresponding to each of the following eight input frequencies: [1 kHz, 2kHz, 3kHz, 4 kHz, 6.5 kHz,
7.5 kHz, 8.5 kHz, and 9.5 kHz.
5. MathScript provides various functions that return
b
and
a
coefficients that can be used to im-
plement filters of various types, such as lowpass, highpass, bandpass, and notch. The frequency arguments
for such functions are given in normalized frequency. For example, the function
fir
1
(N, W n)
where
N
is the filter order (one fewer than the filter or impulse response length that will be provided
as
b
), and
Wn
is the normalized frequency specification. Lowpass and highpass filter impulse responses
that have cutoffs at one-half the Nyquist rate, for example, and a length of 21 samples (for example), can
be obtained by making the call
b
=
b = fir1(20,0.5)
for the lowpass filter, and
b = fir1(20,0.5,'high')
for the highpass filter.
Likewise, bandpass or notch filters of length 31, for example, and band limits of 0.4 and 0.6 (for
example) can be obtained with the call
b = fir1(30,[0.4,0.6])
for the bandpass filter and
b = fir1(30,[0.4,0.6],'stop')
for the notch filter.
For the following sequence sample rates, desired filter length, and desired actual frequency cutoff
limits, design the call for the
fir
1 function; verify the filter function by filtering a chirp of frequency
range 0 to the respective Nyquist rate with the impulse response by using the MathScript function
filter
.
(a) SR = 25,000; filter length = 37; [7000] (lowpass)
(b) SR = 35,000; filter length = 47; [11000] (lowpass)
(c) SR = 44,100; filter length = 107; [5000,8000] (bandpass)
(d) SR = 48,000; filter length = 99; [65] (high)
(e) SR = 8,000; filter length = 47; [800,1200] (notch)
6. What normalized frequency will generate a complex exponential exhibiting one cycle for every
