From the category archives:

Transmitter

Minimum frequency spacing for having orthogonal sinusoidals

In this post, the objective is to figure out the minimum separation between two sinusoidals having frequencies , of duration each to be orthogonal. Let the phase difference between the sinusoidals is where can take any value from to (Refer Example 4.3 [DIG-COMM-SKLAR]).
For the two sinuosidals to be orthogonal,

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Scaling factor in QAM

When QAM (Quadrature Amplitude Modulation) is used, typically one may find a scaling factor associated with the constellation mapping operation. It may be reasonably obvious that this scaling factor is for normalizing the average energy to one.
This post attempts to compute the average energy of the 16-QAM, 64-QAM and M-QAM constellation (where is a [...]

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2nd order sigma delta modulator

In a previous post, the variance of the in-band quantization noise for a first order sigma delta modulator was derived. Taking it one step furhter, let us find the variance of the quantization noise filtered by a second order filter.
With a first order filter, the quantization noise passes through a system with transfer function [...]

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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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Modifying transmit signal

In DSP-Proakis, I found the problem 2.56 interesting as it provides insight into delta modulation. The task is to show that,

where
is any discrete time signal and
is the unit step function.

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