DSP Lab Experiments - Digital Signal Processing: An Introduction with MATLAB and Applications - page 347

(C) 3D plotting
Plot the function z(x, y) = cos(x)exp(- |y|) and its first derivatives. Plot a few
2D cross-sections of z.
(D) Computation algorithms are of fundamental importance in designing new
generations of faster and more efficient computers and digital signal
processors (DSP). Mersenne primes (MP's) are important in computation
algorithms and hardware as they enable binary arithmetic while using
''Number Theoretic Transforms''. An integer m is a Mersenne Primeif it is a
prime number of the form m 5 2p 2 1, where p is a prime. There are only 44
MP's discovered so far. The first 9 MP's are 3, 7, 31, 127, 8191, 131071,
524287, 2147483647, 2305843009213693951 (corresponding to p 5 2, 3, 5,
7, 13, 17, 19, 31, 61), while the last known MP is m44 5 232582657 2 1
(discovered in 2006 and is composed of 9808358 digits). Write a MATLAB
code to find the first 5 MP's.

Part 2: System Implementation

Choose Project-2a or Project-2b as follows.

Project-2a: Hardware Design of Digital Systems

I. Design a digital integrating or differentiating circuit. Using ADC/DAC,

apply analog sinusoids (from a signal generator) with different frequencies
and find the magnitude and phase spectra. Verify the function of the circuit
on the oscilloscope.

II. Design a first-order digital phase-locked loop or a digital delta modulation

system and verify the circuit operation using a sinusoidal signal generator
and an oscilloscope.

Project-2b: Software Analysis of the Sinusoidal Digital Phase-Locked Loop

A: Frequency Tracking of a Sinusoid
Task 1: Noise-Free Analysis
Using MATLAB, simulate the 1st-order sinusoidal DPLL shown in Fig. D.19
Consider a sinusoidal input signal, plot the locking range of the loop, and study the
loop behavior for different circuit parameters. Consider the phase plane, the
sampling process and the transient phase and frequency. For a fixed frequency
ratio W and initial phase (but different combinations), find the effect of the loop
gain K 1 on the locking speed. Locking is practically reached when the difference