Discrete Frequency

Complex sinusoids drawn to highlight the discrete frequency axis k on the left side

An Analog to Digital Converter (ADC) samples a continuous-time signal to produce discrete-time samples. For a digital signal processor, this signal just resides in memory as a sequence of numbers. Consequently, the knowledge of the sample rate $F_S$ is the…
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Additive White Gaussian Noise (AWGN)

Computing noise power within a specified bandwidth

The performance of a digital communication system is quantified by the probability of bit detection errors in the presence of thermal noise. In the context of wireless communications, the main source of thermal noise is addition of random signals arising…
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Modulation – From Numbers to Signals

Wired and wireless channels

The purpose of digital communications is to send digital data across a channel which can be wireless telephone lines coaxial cable optical fiber Ethernet USB chips on a printed circuit board Considering the examples shown in Figure above, clearly neither…
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Transforming a Signal

Pacman circularly shifting to the right

Transforming a discrete-time signal — whether in time or amplitude — is certainly possible, and often in interesting ways. In practice, scaling and time shifting are the two most important signal modifications encountered. Scaling changes the values of dependent variable…
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System Characterization

Magnitude of frequency response |H[k]| in response to complex sinusoids at all N frequencies

After learning some properties of the system, the question is: how should we characterize a system in both time and frequency domains? Impulse response is a tool to characterize a system in time domain and frequency response to do the…
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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.