Why OFDM subcarriers are orthogonal — the math behind the “O”
OFDM subcarriers are orthogonal over a symbol period; how that yields independent flat bins after the DFT, and how CP protects that orthogonality.
Signal Processing
Spectrogram Analysis using Python
Keywords: Spectrogram, signal processing, time-frequency analysis, speech recognition, music analysis, frequency domain, time domain, python Introduction A spectrogram is a visual representation of the frequency content of a signal over time. Spectrograms are widely used in signal processing applications to analyze and visualize time-varying signals, such as speech and audio signals. In this article, we … Read more
Line code – demonstration in Matlab and Python
Line code is the signaling scheme used to represent data on a communication line. There are several possible mapping schemes available for this purpose. Lets understand and demonstrate line code and PSD (power spectral density) in Matlab & Python. Line codes – requirements When transmitting binary data over long distances encoding the binary data using … Read more
Window function figures of merit — scalloping, sidelobes, and ENBW
Compare FFT windows by scalloping loss, sidelobe level, 3 dB bandwidth, and ENBW — and when to pick Hann vs Blackman-Harris vs flattop.
Equivalent noise bandwidth (ENBW) of FFT windows — formula & table
What ENBW means for FFT windows, the time-domain formula used in code, ENBW in bins for common windows, Python (SciPy), and how it shifts the noise floor.
Parseval’s theorem — energy in time equals energy in frequency
Parseval’s theorem (Plancherel): sum/integral of |x|² equals sum/integral of |X|² (with consistent DFT scaling). Derivation intuition and FFT checks.
Statistical measures for stochastic signals
Key focus: Discuss statistical measures for stochastic signals : mean, variance, skewness, kurtosis, histogram, scatterplot, cross-correlation and auto-correlation. Deterministic and stochastic signals A deterministic signal is exactly predictable for the given time span of interest. It could be expressed using analytic form (example: x(t) = sin (2 π fc t) ). Many of the signals … Read more
Design FIR filter to reject unwanted frequencies
Let’s see how to design a simple digital FIR filter to reject unwanted frequencies in an incoming signal. As a per-requisite, I urge you to read through this post: Introduction to digital filter design Background on transfer function The transfer function of a system provides the underlying support for ascertaining vital system response characteristics without … Read more
Digital filter design – Introduction
Key focus: Develop basic understanding of digital filter design. Learn about fundamentals of FIR and IIR filters and the design choices. Analog filters and digital filters are the two major classification of filters, depending on the type of signal signal they process. An analog filter, processes continuous-time signal analog signals. Whereas, digital filters process sampled, … Read more
Plot audio file as time series using Scipy python
Often the most basic step in signal processing of audio files, one would like to visualize an audio sample file as time-series data. Audio sounds can be thought of as an one-dimensional vector that stores numerical values corresponding to each sample. The time-series plot is a two dimensional plot of those sample values as a … Read more