DFT Examples

Magnitude and phase of the DFT of a rectangular signal for L = 7, N= 16 and starting sample shifted by one

For understanding what follows, we need to refer to the Discrete Fourier Transform (DFT) and the effect of time shift in frequency domain first. Here, we discuss a few examples of DFTs of some basic signals that will help not…
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What is Communications?

Wired and wireless channels

"The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point." Claude Shannon – A Mathematical Theory of Communication Our main purpose is to transfer digital information – which…
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Convolution

A signal broken down into scaled and shifted impulses

Understanding convolution is the biggest test DSP learners face. After knowing about what a system is, its types and its impulse response, one wonders if there is any method through which an output signal of a system can be determined…
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Modulation Bandwidths

Square-Root Raised Cosine (SR-RC) spectrum with different excess bandwidths

From the article on pulse shaping, we can correctly determine the occupied bandwidth for each modulation scheme where the Square-Root Raised Cosine spectrum shows the bandwidth of a Square-Root Raised Cosine pulse shape as $0.5(1+\alpha)R_M$. Also, we have discussed earlier…
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Sample Rate Conversion

A rectangular signal and its upsampled version in time and frequency domains

In the discussion on sampling, the process of sampling a continuous-time signal was discussed in detail and subsequently sampling theorem was derived. In many applications, resampling an already digitized signal is mandatory for an efficient system design. In wireless communications,…
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There are 26 letters in English language and countless rules. The language of signal processing is simpler.

- It has only 1 letter: a sample at time 0. From there, we can build any discrete-time signal on which our 1s and 0s can be mapped.

- It has one major rule which is repeatedly employed for demapping the received signal to bits.


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