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Unformatted text preview: LTI h(n) Introduction Digital signal processing ( DSP ) is the study of signals in a digital representation and the processing methods of these signals. DSP and analog signal processing are subfields of signal processing . DSP includes subfields like: audio and speech signal processing , sonar and radar signal processing, sensor array processing, spectral estimation, statistical signal processing, digital image processing , signal processing for communications, biomedical signal processing, seismic data processing, etc. Processing of such signals includes storage and reconstruction, separation of information from noise (for example, aircraft identification by radar), compression (for example, image compression ), and feature extraction (for example, speech-to-text conversion). Since the goal of DSP is usually to measure or filter continuous real-world analog signals, the first step is usually to convert the signal from an analog to a digital form, by using an analog to digital converter . Often, the required output signal is another analog output signal, which requires a digital to analog converter . Filtering is done by the filters whose magnitude response and phase response specifies particular specifications in frequency domain. The term adaptive filtering implies the filter parameters such as band width that vary with the time. The unwanted signal that is been mixed with the signal, this noise should be reduced or removed by using filters. If the signal and noise occupy the fixed and separate frequency bands for these linear filters are suited. The signal or noise spectra vary with the time then adaptive filters are suitable. Digital Filters are broadly classified into two types Finite impulse response (FIR) Infinite Impulse response (IIR). Finite Impulse response (FIR) In the finite impulse response filters response depends only on the past and present input samples. An FIR can be implemented almost any sort of frequencies digitally. The impulse response of a FIR filter of Nth order will have N+1 samples for the next sample it becomes zero. Where y[n] is the output signal X[n] is the input signal Bi is the filter coefficient and N is the order of the filter FIR filters are generally stable because all the poles are located at the origin that defines that they are located within the unit circle. The main advantage of Finite impulse response is that they are designed to have linear phase that they are preserved with input signal with wave shape. The main disadvantages of this FIR filter are that that they have many coefficients to reach the same frequency response, for this they require large memory usage and large time for process Infinite Impulse Response (IIR) An infinite impulse response filter produces an output which is the weighted sun of present and past input as well as the past outputs. As IIR is in infinite loop the impulse response from an IIR digital filter decays to zero and goes to infinity. If X(z) is the input z transform of the signal, Y(z) is digital filter decays to zero and goes to infinity....
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- Spring '09