Digital Signal Processing

 Digital signal processing (DSP) is the mathematical manipulation of an information signal to modify or improve it by some way. It is characterized by the representation of discrete time, discrete frequency, or other discrete domain signals by a sequence of numbers or symbols and the processing of these signals.DSP is usually to measure, filter and/or compress continuous real-world analog signals.In this firstly analog signal are converted into digital signal by sampling and then digitizing it using an analog-to-digital converter (ADC).

DSP Applications:-
1.audio and speech signal processing.
2.sonar and radar signal processing, sensor array processing
3.DSP algorithms have long been run on standard computers, as well as on specialized processors called digital signal processors.
4.spectral estimation, statistical signal processing.

In DSP

Digitalization have main role , that done with help of signal sampling.According to the Nyquist–Shannon sampling theorem states that a signal can be exactly reconstructed from its samples if the sampling frequency is greater than twice the highest frequency of the signal, but this requires an infinite number of samples. In practice, the sampling frequency is often significantly higher than twice that required by the signal's limited bandwidth.
In DSP, engineers usually study digital signals in one of the following domains: time domain (one-dimensional signals), spatial domain (multidimensional signals), frequency domain, and wavelet domains(A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases, and then decreases back to zero.)A sequence of samples from a measuring device produces a temporal or spatial domain representation, whereas a discrete Fourier transform produces the frequency domain information, that is, the frequency spectrum.

Time Domain:- The most common processing approach in the time or space domain is enhancement of the input signal through a method called filtering. There are various ways to characterize Digital filters. E.g.

1.A "linear" filter is a linear transformation of input samples; other filters are "non-linear". Linear filters satisfy the superposition condition, i.e. if an input is a weighted linear combination of different signals, the output is a similarly weighted linear combination of the corresponding output signals.

2. A "causal" filter uses only previous samples of the input or output signals; while a "non-causal" filter uses future input samples. A non-causal filter can usually be changed into a causal filter by adding a delay to it.

3.A "time-invariant" filter has constant properties over time; other filters such as adaptive filters change in time.

4.A "stable" filter produces an output that converges to a constant value with time, or remains bounded within a finite interval. An "unstable" filter can produce an output that grows without bounds, with bounded or even zero input.

5.A "finite impulse response" (FIR) filter uses only the input signals, while an "infinite impulse response" filter (IIR) uses both the input signal and previous samples of the output signal. FIR filters are always stable, while IIR filters may be unstable.

Frequency Domain:-Signals are converted from time or space domain to the frequency domain usually through the Fourier transform. The Fourier transform converts the signal information to a magnitude and phase component of each frequency.The main motive for analysis of signals in the frequency domain is analysis of signal properties.

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