Signal Processing for Communication Systems
“What is the best filter that I should use? FIR or IIR ?” is often the question asked by many. There exists two different types of Linear Time Invariant (LTI) filters from transfer function standpoint : FIR (Finite Impulse Response) and IIR (Infinite Impulse Response) filters and myriad design techniques for designing them. The mere fact … Read more
Key focus: With examples, let’s estimate and plot the probability density function of a random variable using Matlab histogram function. Generation of random variables with required probability distribution characteristic is of paramount importance in simulating a communication system. Let’s see how we can generate a simple random variable, estimate and plot the probability density function … Read more
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
In the previous post, Interpretation of frequency bins, frequency axis arrangement (fftshift/ifftshift) for complex DFT were discussed. In this post, I intend to show you how to interpret FFT results and obtain magnitude and phase information. Outline For the discussion here, lets take an arbitrary cosine function of the form \(x(t)= A cos \left(2 \pi … Read more
Key focus: Interpret FFT results, complex DFT, frequency bins, fftshift and ifftshift. Know how to use them in analysis using Matlab and Python. Four types of Fourier Transforms: Often, one is confronted with the problem of converting a time domain signal to frequency domain and vice-versa. Fourier Transform is an excellent tool to achieve this … Read more
Root Mean Square (RMS) value is the most important parameter that signifies the size of a signal. Defining the term “size”: In signal processing, a signal is viewed as a function of time. The term “size of a signal” is used to represent “strength of the signal”. It is crucial to know the “size” of … Read more
In this article, the relationship between SNR-per-bit (Eb/N0) and SNR-per-symbol (Es/N0) are defined with respect to M-ary signaling schemes. Then the complex baseband model for an AWGN channel is discussed, followed by the theoretical error rates of various modulations over the additive white Gaussian noise (AWGN) channel. Finally, the complex baseband models for digital modulators … 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
This article focused on constructing constellation for rectangular QAM modulation using Karnaugh-map walks. Exploit inherent property of Karnaugh-maps to construct Gray coded QAM constellation points. M-ary Quadrature Amplitude Modulation (M-QAM) In MQAM modulations, the information bits are encoded as variations in the amplitude and the phase of the signal. The M-QAM modulator transmits a series … Read more
Key focus: Know how to generate a Chirp signal, compute its Fourier Transform using FFT and power spectral density (PSD) in Matlab & Python. Introduction All the signals discussed so far do not change in frequency over time. Obtaining a signal with time-varying frequency is of main focus here. A signal that varies in frequency … Read more