In this post, we implement two basic image transformations in MATLAB: converting a colour image to grayscale and producing its digital negative. The digital negative inverts the intensity of every pixel — dark areas become light and vice versa — by applying the transformation s = 255 - r to each pixel value r. These are fundamental point processing operations in digital image processing.
MATLAB Code
% Digital Negative and Grayscale of an Image in MATLAB
% Demonstrates two point-processing transformations:
% 1. RGB -> Grayscale
% 2. Grayscale -> Digital Negative
clc; % Clear the command window
clear all; % Clear all workspace variables
% --- Load the image ---
% Place your image in the MATLAB working directory.
originalImage = imread('desert.jpg'); % Read a colour (RGB) image
% --- Convert to Grayscale ---
grayImage = rgb2gray(originalImage); % Average the R, G, B channels
% --- Compute Digital Negative ---
% For an 8-bit image the maximum intensity is 255.
% Negative: negative(x,y) = 255 - gray(x,y)
negativeImage = 255 - grayImage;
% Optionally save the negative image to disk
imwrite(negativeImage, 'negative.jpg');
% --- Display all three images side by side ---
subplot(1, 3, 1);
imshow(originalImage);
title('Original Colour Image');
subplot(1, 3, 2);
imshow(grayImage);
title('Grayscale Image');
subplot(1, 3, 3);
imshow(negativeImage);
title('Digital Negative');
In this post, we implement gray-level slicing in MATLAB — a point processing technique used in digital image processing to highlight a specific range of gray levels while suppressing everything outside that range. The program reads a grayscale image, asks the user to specify a lower and upper gray-level boundary, and produces two sliced images: one that preserves the background and one that blacks it out.
MATLAB Code
% Gray-Level Slicing in MATLAB
% Highlights pixels within a user-defined gray-level range.
% Two sliced versions are produced:
% b - background preserved (pixels below r1 unchanged)
% c - background suppressed (only the range [r1,r2] is shown in white)
clc; % Clear the command window
clear all; % Clear all workspace variables
% --- Load image ---
% Place your image file in the MATLAB working directory.
originalImage = imread('sample.jpg'); % Read the image file
grayImage = rgb2gray(originalImage); % Convert to grayscale
imageSize = size(grayImage); % [rows, cols]
% --- User inputs ---
lowerLevel = input('Enter lower gray level : '); % e.g. 20
upperLevel = input('Enter upper gray level : '); % e.g. 50
% --- Slicing: preserve background ---
% Pixels above upperLevel are set to 255 (white); others stay the same.
slicedPreserve = grayImage;
for row = 1:imageSize(1)
for col = 1:imageSize(2)
if grayImage(row, col) > lowerLevel
if grayImage(row, col) > upperLevel
slicedPreserve(row, col) = 255; % Highlight bright pixels
end
end
end
end
% --- Slicing: suppress background ---
% Pixels inside [lowerLevel, upperLevel] -> white; outside -> black.
slicedSuppress = grayImage;
for row = 1:imageSize(1)
for col = 1:imageSize(2)
if grayImage(row, col) > lowerLevel
if grayImage(row, col) > upperLevel
slicedSuppress(row, col) = 255; % In range -> white
else
slicedSuppress(row, col) = 0; % Out of range -> black
end
end
end
end
% --- Display all three images side by side ---
subplot(1, 3, 1);
imshow(grayImage);
title('Original Grayscale');
subplot(1, 3, 2);
imshow(slicedPreserve);
title('Sliced (Background Preserved)');
subplot(1, 3, 3);
imshow(slicedSuppress);
title('Sliced (Background Suppressed)');
In this post, we plot the discrete-time sine and cosine functions in MATLAB using the stem() function. Sine and cosine are the most fundamental periodic signals in signal processing. Visualising them in the discrete-time domain helps build intuition for sampling, frequency analysis, and filter design.
MATLAB Code
% Plotting Discrete-Time sin and cos in MATLAB
% The user supplies n; the time axis runs from -n to +n.
clc; % Clear the command window
clear all; % Clear all workspace variables
% --- Sine plot ---
nSin = input('Enter n for sin plot : '); % e.g. 5
tSin = -nSin:1:nSin; % Time axis: -n, ..., 0, ..., +n
ysin = sin(tSin); % Compute sin at each sample
subplot(1, 2, 1);
stem(tSin, ysin);
title('sin(n)');
xlabel('n');
ylabel('Amplitude');
ylim([-1.5, 1.5]); % Fix y-axis for readability
% --- Cosine plot ---
nCos = input('Enter n for cos plot : '); % e.g. 5
tCos = -nCos:1:nCos; % Time axis: -n, ..., 0, ..., +n
ycos = cos(tCos); % Compute cos at each sample
subplot(1, 2, 2);
stem(tCos, ycos);
title('cos(n)');
xlabel('n');
ylabel('Amplitude');
ylim([-1.5, 1.5]); % Fix y-axis for readability
In this post, we use MATLAB to plot four fundamental discrete-time signals: the Unit Impulse, Unit Step, Unit Ramp, and Exponential Function. These signals are the building blocks of digital signal processing (DSP) and control systems theory. Understanding how to generate and visualize them in MATLAB is the first step towards analyzing more complex systems.
MATLAB Code
% Plotting Unit Impulse, Unit Step, Unit Ramp and Exponential Function
% All four signals are plotted in a 2x2 subplot grid.
clc; % Clear the command window
clear all; % Clear all workspace variables
% --- 1. Unit Impulse (delta function) ---
% Non-zero only at n=0; value = 1 at origin, 0 elsewhere
t = -2:1:2; % Time axis: -2, -1, 0, 1, 2
impulse = [zeros(1,2), 1, zeros(1,2)]; % 1 only at center (t=0)
subplot(2, 2, 1);
stem(t, impulse);
title('Unit Impulse');
xlabel('n');
ylabel('delta(n)');
% --- 2. Unit Step ---
% Value = 1 for all n >= 0
nStep = input('Enter length for unit step : '); % e.g. 5
tStep = 0:1:nStep - 1; % Time axis: 0, 1, ..., nStep-1
stepSignal = ones(1, nStep); % All ones
subplot(2, 2, 2);
stem(tStep, stepSignal);
title('Unit Step');
xlabel('n');
ylabel('u(n)');
% --- 3. Unit Ramp ---
% Value increases linearly: r(n) = n for n >= 0
nRamp = input('Enter length for unit ramp : '); % e.g. 4
tRamp = 0:1:nRamp - 1; % Time axis: 0, 1, ..., nRamp-1
subplot(2, 2, 3);
stem(tRamp, tRamp); % y = n (ramp equals the index)
title('Unit Ramp');
xlabel('n');
ylabel('r(n) = n');
% --- 4. Exponential Function ---
% y(n) = exp(a*n); decaying when a0
nExp = input('Enter length for exponential : '); % e.g. 5
tExp = 0:1:nExp - 1; % Time axis
a = input('Enter exponent value (a) : '); % e.g. -0.5 or 2
expSignal = exp(a * tExp);
subplot(2, 2, 4);
stem(tExp, expSignal);
title('Exponential Function');
xlabel('n');
ylabel('e^{an}');
In this post, we implement Linear Convolution and Circular Convolution in MATLAB and plot both results side by side. Convolution is a fundamental operation in signal processing used to find the output of a Linear Time-Invariant (LTI) system when an input signal is applied to it.
Linear convolution computes the full convolution of two sequences, producing an output of length M + N - 1. Circular convolution (also called cyclic convolution) wraps around the result and is the basis of fast frequency-domain filtering using the DFT.
MATLAB Code
% Linear and Circular Convolution in MATLAB
% Reads two sequences from the user, computes both convolutions,
% displays the numerical results and plots all four signals.
clc; % Clear the command window
clear all; % Clear all workspace variables
% --- Input ---
x = input('Enter first sequence : '); % e.g. [1 1 2 2]
y = input('Enter second sequence : '); % e.g. [1 2 3 4]
% --- Linear Convolution ---
% conv() returns a vector of length length(x)+length(y)-1
z = conv(x, y);
disp('Linear convolution result:');
disp(z);
% --- Circular Convolution ---
% cconv(x, y) uses the length of the longer sequence by default
c = cconv(x, y);
disp('Circular convolution result:');
disp(c);
% --- Plot all four signals ---
figure;
subplot(4, 1, 1);
stem(x);
title('First Input Sequence (x)');
xlabel('Sample Index');
ylabel('Amplitude');
subplot(4, 1, 2);
stem(y);
title('Second Input Sequence (y)');
xlabel('Sample Index');
ylabel('Amplitude');
subplot(4, 1, 3);
stem(z);
title('Linear Convolution (z = x * y)');
xlabel('Sample Index');
ylabel('Amplitude');
subplot(4, 1, 4);
stem(c);
title('Circular Convolution (c = x ⊛ y)');
xlabel('Sample Index');
ylabel('Amplitude');
