DSP Lab Experiments - Digital Signal Processing: An Introduction with MATLAB and Applications - page 332

Task 3

Define the system true time and plot the theoretical impulse response as in Eq. 1 .

Task 4

Analyze the system using tf , impulse , and freqz . Plot all results.

Task 5

Now simulate the oscillator circuit as shown in Fig. D.6 . Enter a delta signal and
find the output. Plot and compare with previous methods of finding the impulse
response.

Task 6

Find the effect of changing the sampling frequency on the system. Reduce the
sampling frequency to 10 Hz and compare.

Task 7

With f s = 100 Hz and A = 1, try to generate 2, 10, 45, 60, and 70 Hz sinusoids.
See what happen if f o [ f s /2. Change the amplitude and plot the resulting output
signals.

Experiment # 6: Sampling and Reconstruction

Introduction

To process analog (i.e., continuous-time) signals using digital technology, we
should convert these signals into digital signalsthrough sampling and A/D
conversion. In most applications, sampling is uniform, i.e., the sampling interval T s
and the sampling frequency, f s = 1/T s , are constant. Ideal sampling can be
formulated as multiplication of the analog signal x(t) by the a train of time
impulses p ð t Þ¼ P 1

n ¼1 d ð t nT s Þ as shown in Fig. D.8 The spectrum of this

time impulse train is the frequency impulse train P ð f Þ¼ f s P k ¼1 d ð f kf s Þ .
The above multiplication in the time domain would be a convolution in the
frequency domain between the frequency impulse train and the spectrum of the
analog signal, X(f), which results in the scaling (by f s ) and repetition (every f s )of
this spectrum as shown in Fig. D.9 , where we used the normalized frequency
v = f/f s . The new spectrum is called the discrete-time Fourier transform (DTFT).
Reconstruction of the sampled signal (back to the analog signal) is possible