Signal Processing for Communication Systems
Synopsis: Cyclic prefix in OFDM, tricks a natural channel to perform circular convolution. This simplifies equalizer design at the receiver. Hands-on demo in Matlab. Cyclic Prefix-ed OFDM A cyclic-prefixed OFDM (CP-OFDM) transceiver architecture is typically implemented using inverse discrete Fourier transform (IDFT) and discrete Fourier transform (DFT) blocks (refer Figure 13.3). In an OFDM transmitter, … Read more
Auto-correlation, also called series correlation, is the correlation of a given sequence with itself as a function of time lag. Cross-correlation is a more generic term, which gives the correlation between two different sequences as a function of time lag. Given two sequences and , the cross-correlation at times separated by lag i is given … Read more
Mathematical details of convolution, its relationship to polynomial multiplication and the application of Toeplitz matrices in computing linear convolution are discussed in the previous article. A short survey of different techniques to compute discrete linear convolution (with Matlab code) is given here. Definition Given an LTI (Linear Time Invariant) system with impulse response \(h[n]\) and … Read more
Convolution operation is ubiquitous in signal processing applications. The mathematics of convolution is strongly rooted in operation on polynomials. The intent of this text is to enhance the understanding on mathematical details of convolution. Polynomial functions: Polynomial functions are expressions consisting of sum of terms, where each term includes one or more variables raised to … Read more