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first order

First order digital PLL for tracking constant phase offset

Considering a typical scenario where there might exist a small phase offset between local oscillator between the transmitter and receiver.

Figure 1 :
Transmitter receiver with constant phase offset
In such cases, it might be desirable to estimate and track the phase offset such that the performance of the receiver does not degrade.

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Sigma delta modulation

In an earlier post, it was mentioned that delta modulator without the quantizer is identical to convolving an input sequence with . Let us first try to validate that thought using a small MATLAB example and using the delta modulator circuit shown in Figure 9.13a of DSP-Proakis [1].
% delta modulation
xn = sin(2*pi*1/64*[0:63]);
xhatn = 0;

for [...]

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Zero-order hold and first-order hold based interpolation

In problem 9.14 of DSP-Proakis, the objective is to analyze the effect of zero-order interpolation and first-order interpolation to double the number of samples in the sinusoidal
while keeping the sampling frequency unchanged.
My take:
The first part of the problem (a) is to generate the sequence having half the frequency of . For zero-order [...]

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