How to add an echo effect to an audio signal using Matlab

In this post I explain how to add an echo to an audio signal using Matlab. If you closely look at the below code, you can understand, what kind of a process is there. Initially the original signal x is delayed by 0.5 seconds and then multiplied by the attenuation constant alpha(0.65) to reduce the amplitude of the echo signal. Finally the delayed and attenuated signal is added back to the original signal to get the echo effect of the audio signal. You can visualize this process using the below mentioned Matlab simulink model.

Matlab code

 clear all;  
 %% Hallelujah Chorus  
 [x,Fs] = audioread('Hallelujah.wav');  
 sound(x,Fs);  
 pause(10);  
 delay = 0.5; % 0.5s delay  
 alpha = 0.65; % echo strength  
 D = delay*Fs;  
 y = zeros(size(x));  
 y(1:D) = x(1:D);  
   
 for i=D+1:length(x)  
   y(i) = x(i) + alpha*x(i-D);  
 end  
   
 %% using filter method.  
 % b = [1,zeros(1,D),alpha];  
 % y = filter(b,1,x);  
   
 %% echoed Hallelujah Chorus  
 sound(y,Fs);  

 * You can download Hallelujah.wav from here or else you can find more .wav files from WavSource.com. Varying the value of alpha would change the echo strength of the audio signal.

Original and echoed audio signals in Audacity

You can create the Matlab simulink model for echo generation as follows.

Matlab simulink model for echo generation

Model parameters

• From Multimedia File 

samples per audio channel - 8192
Audio output sampling mode - Frame based
Audio output data type - double

• Gain

 Gain - 0.65

• Delay

Delay length - 4096
Input Processing - Columns as channels (frame based)

* If you use any other .wav file other than Hallelujah.wav, then you should change the above parameters accordingly.

Frequency Divider

A frequency divider, also called a clock divider or scaler or prescaler, is a circuit that takes an input signal of a frequency, fin, and generates an output signal of a frequency :

Source - Wikipedia

Where n is an integer (Wikipedia). In this post I explain how to implement the digital design of a simple clock divider(fin/2).

Source - ElectronicsTutorials

Verilog module

 module clock_divider (clk_in, enable,reset, clk_out);  
   input clk_in; // input clock  
   input reset;  
   input enable;  
   output clk_out; // output clock  
   
   wire  clk_in;  
   wire  enable;  
   
   reg clk_out;  
   
   always @ (posedge clk_in)  
     if (reset)  
       begin  
         clk_out <= 1'b0;  
       end  
     else if (enable)  
       begin  
         clk_out <= !clk_out ;  
       end  
   
 endmodule  

Test-bench

 module tb_clock_divider;  
   reg clk_in, reset,enable;  
   wire clk_out;  
     
   clock_divider U0 (  
    .clk_in (clk_in),  
    .enable(enable),  
    .reset (reset),  
    .clk_out (clk_out)  
   );  
     
   initial  
     begin  
       clk_in = 0;  
       reset = 0;  
       enable = 1;  
       #10 reset = 1;  
       #10 reset = 0;  
       #100 $finish;  
     end  
       
   always #5 clk_in = ~clk_in;  
     
 endmodule  

Simulation results

Elaborated design

Verilog simulation and RTL analysis was done in Vivado 2014.2. If you want to divide the input frequency further, (fin/4, fin/8, fin/16), you can extend the same circuit as follows.
 

Source - ElectronicsTutorials

Merge Sort

The basic idea of the algorithm is to split the collection into smaller groups by halving it until the groups only have one element or no elements (which are both entirely sorted groups). Then merge the groups back together so that their elements are in order (Rosetta code). Merge sort follows divide-and-conquer approach.

Worst case performance - O(n log n)

Source - Wikipedia

 C++

 void merge_sort(int array[], int low, int high)  
 {  
   if (low < high)  
   {  
     int middle = (low + high) / 2;  
     merge_sort(array,low, middle);  
     merge_sort(array,middle + 1, high);  
     merge(array, low, middle, high);  
   }  
 }  
   
 void merge(int array[], int low, int middle, int high)  
 {  
   int size1 = middle - low + 1;  
   int size2 = high - middle;  
   int left[size1 + 1];  
   int right[size2 + 1];  
   for (int i = 0; i < size1; i++)  
   {  
     left[i] = array[low + i];  
   }  
   for (int j = 0; j < size2; j++)  
   {  
     right[j] = array[middle + j + 1];  
   }  
   left[size1] = numeric_limits<int>::max();;  
   right[size2] = numeric_limits<int>::max();;  
   int i = 0;  
   int j = 0;  
   for (int k = low; k <= high; k++)  
   {  
     if (left[i] <= right[j])  
     {  
       array[k] = left[i];  
       i++;  
     }  
     else  
     {  
       array[k] = right[j];  
       j++;  
     }  
   }  
 }   

Java

   static int[] array = {5, 4, 8, 3, 1, 2, 9, 6, 7, 10};  
   
   static void merge_sort(int[] array, int low, int high) {  
       if (low < high) {  
         int middle = (low + high) / 2;  
         merge_sort(array, low, middle);  
         merge_sort(array, middle + 1, high);  
         merge(array, low, middle, high);  
       }  
    }  
   
   static void merge(int[] array, int low, int middle, int high) {  
       int size1 = middle - low + 1;  
       int size2 = high - middle;  
       int[] left = new int[size1 + 1];  
       int[] right = new int[size2 + 1];  
       for (int i = 0; i < size1; i++) {  
         left[i] = array[low + i];  
       }  
       for (int j = 0; j < size2; j++) {  
         right[j] = array[middle + j + 1];  
       }  
       left[size1] = Integer.MAX_VALUE;  
       right[size2] = Integer.MAX_VALUE;  
       int i = 0;  
       int j = 0;  
       for (int k = low; k <= high; k++) {  
         if (left[i] <= right[j]) {  
           array[k] = left[i];  
           i++;  
         } else {  
           array[k] = right[j];  
           j++;  
         }  
       }  
    }  

Matlab

   function array = merge_sort(array,low,high)  
     if(low < high)  
       middle = floor((low + high)/2);  
       array = merge_sort(array,low, middle);  
       array = merge_sort(array,middle + 1, high);  
       array = merge(array, low, middle, high);  
     end  
   end  
   
   function array = merge(array,low,middle,high)  
     size1 = middle - low + 1;  
     size2 = high - middle;  
     left = zeros(1,size1+1);  
     right = zeros(1,size2+1);  
     for i=1:size1  
       left(i) = array(low+i-1);  
     end  
     for j=1:size2  
       right(j) = array(middle+j);  
     end  
     left(size1+1) = inf;  
     right(size2+1) = inf;  
     i = 1;  
     j = 1;  
     for k=low:high  
       if left(i)<= right(j)  
         array(k) = left(i);  
         i = i + 1;  
       else  
         array(k) = right(j);  
         j = j + 1;  
       end  
     end  
   end   

Python 

import math

def merge(array,low,middle,high):
    size1 = middle - low + 1
    size2 = high - middle
    left = [0]* (size1+1)
    right = [0]* (size2+1)
    for i in range(size1):
        left[i] = array[low+i]
    for j in range(size2):
        right[j] = array[middle+j+1]
    left[size1] = float("inf")
    right[size2] = float("inf")
    i = 0
    j = 0
    for k in range(low,high+1):
        if left[i]<= right[j]:
            array[k] = left[i]
            i = i + 1
        else:
            array[k] = right[j]
            j = j + 1
   
def merge_sort(array,low,high):
    if low<high:
        middle = int(math.floor((low+high)/2))
        merge_sort(array,low,middle)
        merge_sort(array,middle+1,high)
        merge(array,low,middle,high)