Tutorials Archives - GaussianWaves

Matplotlib histogram and estimated PDF in Python

Mathuranathan — Fri, 05 Jun 2020 08:28:31 +0000

Key focus: Shown with examples: let’s estimate and plot the probability density function of a random variable using Python’s Matplotlib 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 ... Read more

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Linear regression using python – demystified

Mathuranathan — Wed, 05 Feb 2020 06:52:00 +0000

Key focus: Let’s demonstrate basics of univariate linear regression using Python SciPy functions. Train the model and use it for predictions. Linear regression model Regression is a framework for fitting models to data. At a fundamental level, a linear regression model assumes linear relationship between input variables () and the output variable (). The input ... Read more

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Generating simulated dataset for regression problems

Mathuranathan — Fri, 31 Jan 2020 03:00:12 +0000

Key focus: Generating simulated dataset for regression problems using sklearn make_regression function (Python 3) is discussed in this article. Problem statement Suppose, a survey is conducted among the employees of a company. In that survey, the salary and the years of experience of the employees are collected. The aim of this data collection is to ... Read more

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Plot audio file as time series using Scipy python

Mathuranathan — Thu, 23 Jan 2020 07:41:29 +0000

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

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Plot FFT using Python – FFT of sine wave & cosine wave

Mathuranathan — Wed, 22 Jan 2020 09:09:05 +0000

Key focus: Learn how to plot FFT of sine wave and cosine wave using Python. Understand FFTshift. Plot one-sided, double-sided and normalized spectrum using FFT. Introduction Numerous texts are available to explain the basics of Discrete Fourier Transform and its very efficient implementation – Fast Fourier Transform (FFT). Often we are confronted with the need ... Read more

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Fibonacci sequence in python – a short tutorial

Mathuranathan — Mon, 20 Jan 2020 04:50:02 +0000

Key focus: Learn to generate Fibonacci sequence using Python. Python 3 is used in this tutorial. Fibonacci series is a sequence of numbers 0,1,1,2,3,5,8,13,… Let’s digress a bit from signal processing and brush up basic some concepts in python programming. Why python? Python is an incredibly versatile programming language that is used for everything from ... Read more

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Phase demodulation via Hilbert transform: Hands-on

Mathuranathan — Tue, 06 Jun 2017 08:28:44 +0000

Key focus: Demodulation of phase modulated signal by extracting instantaneous phase can be done using Hilbert transform. Hands-on demo in Python & Matlab. Phase modulated signal: The concept of instantaneous amplitude/phase/frequency are fundamental to information communication and appears in many signal processing application. We know that a monochromatic signal of form x(t) = a cos(ω ... Read more

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Extract envelope, phase using Hilbert transform: Demo

Mathuranathan — Mon, 24 Apr 2017 08:56:26 +0000

Key focus: Learn how to use Hilbert transform to extract envelope, instantaneous phase and frequency from a modulated signal. Hands-on demo using Python & Matlab. If you would like to brush-up the basics on analytic signal and how it related to Hilbert transform, you may visit article: Understanding Analytic Signal and Hilbert Transform Introduction The ... Read more

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Understanding Analytic Signal and Hilbert Transform

Mathuranathan — Thu, 20 Apr 2017 09:52:00 +0000

Key focus of this article: Understand the relationship between analytic signal, Hilbert transform and FFT. Hands-on demonstration using Python and Matlab. Introduction Fourier Transform of a real-valued signal is complex-symmetric. It implies that the content at negative frequencies are redundant with respect to the positive frequencies. In their works, Gabor [1] and Ville [2], aimed ... Read more

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Interpret FFT results – obtaining magnitude and phase information

Mathuranathan — Thu, 19 Nov 2015 06:02:14 +0000

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

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