Signals can be any time-varying or space-varying quantity. Examples: speech, temperature readings, seismic data, stock price fluctuations. A signal has one or more frequency components in it and can be viewed from two different standpoints: time-domain and frequency domain. In general, signals are recorded in time-domain but analyzing signals in frequency domain makes the task easier.... Continue Reading →

# Complex Moving Waves

In the previous case, we have seen how can we model a simple wave travelling with one frequency. In nature, usually we encounter waves as an ensemble of many frequencies. Here, let us try to add more frequencies in the previous scenario: MATLAB code clear; close all; clc fs=1000; %sampling frequency t=0:1/fs:0.5-1/fs;%time f=[1 2... Continue Reading →

# Modelling Waves (MATLAB)

We can use waves to model almost everything in the world from the thing we can see or touch to the things which we can't. Here, we try to model the waves itself. Moving Waves clear; close all; clc a=1; %amplitude f=5; %frequency T=1/f; %time period w=2*pi*f; %angular frequency lb=2*T; %wavelength k=2*pi/lb;... Continue Reading →

# Seismic Resolution

Seismic resolution and fidelity are the two important measures of the quality of the seismic record and the seismic images. Seismic resolution quantifies the level of precision, such as the finest size of the subsurface objects detectable by the seismic data whereas the seismic fidelity quantifies the truthfulness such as the genuineness of the data... Continue Reading →

# Analytical signal and Hilbert Transform

For a real time series x(t), its analytic signal x(t) is defined as x(t) = x(t) - iH[x(t)] Let us consider an example of a monochromatic signal 𝑥(𝑡) = 5 sin(10𝑡 + 3). Figure 1 Now, let us consider a more complex function x(t) = 1*sin(2𝜋10𝑡 + 0.3) + 2*sin(2𝜋20𝑡 + 0.2) + 3*sin(2𝜋30𝑡 + 0.4). Figure... Continue Reading →

# Aliasing and Nyquist Condition

Let us consider a simple sinusoidal signal x(t) = 5*sin(10*t + 3) This is a signal with amplitude of 5, angular frequency of 10 and phase of 3. The Nyquist condition demands that the angular frequency, mod(𝜔) ≤ pi/delta t. For the above figure 1, we took 𝜔 to be 10 and pi/delta t is 99.5,... Continue Reading →