Speech & Language Blog

Introduction The decibel is a unit to express loudness of sounds, and an important measurement in sound processing. The decibel is the logarithmic scale of sound intensity. The reason to use the logarithm is that human hearing is logarithmic rather than linear. The decibel is also not an absolute metric but a relative ratio of intensity of one sound compared to another. This part is very confusing because we think that familiar measurements like lengths "cm, m, km" and weight "g, kg..." are absolute units. There are many online resources that explain the logarithms or the decibel. I don't see resources that explain both the logarithms and the decibel. This is my motivation to create this post: keeping information about the logarithms and the decibel in one page.  Logarithms The logarithms are inverse operation of an exponent (power). \[ 2^3 = 8 \] \[ \log_28 = 3 \] The log of 8 to the base 2 is 3 , and 2 to...

Discrete Fourier Transform The last part of the previous post mentions the method to find frequencies in a signal: the Discrete Fourier Transform (DFT). This post dives deeper into the DFT. The main idea of the DFT is to find out which frequency component correlates with the given input signal . This mathematical formula looks scary. \[ X[k] = \sum_{n=0}^{N-1} x[n] \, e^{-j2\pi k n / N} \] k = current frequency to check correlation n = current sample N = number of samples x[n] = the value of the current sample of the given signal My goal in this post is to demonstrate what the DFT performs is simple. Input signal and correlation signal Let's say the input signal is a sine wave of 2 Hz. There are 30 samples to represent this signal. The input signal of 2 Hz should show the highest correlation at 2 Hz. Let's also have 5 different correlation signals varying from 0 Hz to 5 Hz. The first correlation signal has i...