Pre–emphasis - Signal Processing

I am trying to compute the Pre-emphasis of a signal and the formular is below:

y[n] = x[n] - 0.95 x[n-1]

Let:

x=[1 3 5 9 4 3 2 1]

First..

x[1] = 1

x[n - 1] =0 

y[n] = 1 - (0.95 * 0) = 1

Second.. 

x[2] = 3

x[n - 1] = 1 

y[n] = 3 - (0.95 * 1) = 2.05

Therefore:

y[n] = 3 - (0.95 * 1) = 2.05
But I don't understand how this has increased the energy of the signal at a higher frequency? Because 3 is greater than 2.05 etc.. 
How this filter work?

[KALYAN ACHARJYA]

Is this Matlab related question or understand the concept?

Answer 1

[Dimitris Kalogiros]

Your question regards frequency response of FIR filters. I suggest to study (and run) the following script.

clear; clc; close all;

%frequency response of a filter with differencial equation  y[n]=x[n]-0.95*x[x-1]
h=[1 -0.95]; 
freqz(h); zoom on; grid on; 
title('frequency response')

%attenuation of a LOW frequency signal
t=0:1:500;
f1=0.01;
x=sin(2*pi*f1*t);
y=filter(h,1,x);
figure; 
plot(x,'-b'); hold on;
plot(y, '-r'); zoom on; grid on;
legend('input', 'output');
title('attenuation of a LOW frequency signal')

%enhancement of a HIGH frequency signal
t=0:1:100;
f1=0.3;
x=sin(2*pi*f1*t);
y=filter(h,1,x);
figure; 
plot(x,'-b'); hold on;
plot(y, '-r'); zoom on; grid on;
legend('input', 'output');
title('enhancement of a HIGH frequency signal');

Which illustrates how your filter works. How it emphasizes high frequencies and attenuates lowers

[craze j]

what is the input in the above code?what is x,y,f1 and what operation is taking place in x,y and f1? why f1 is fixed to that value and t is taken to that range? if speech signal is applied to above code then what input is given and where?

[Dimitris Kalogiros]

I used filter h=[1 -0.95] twice.

Each time, x is the input of the filter and y is the output.

At both examples, x was a sinusoidal signal, with frequency f1.

I use f1, in order to show what frequences are going to be attenuated and what frequencies are going to be enchaned.

t=0:1:500;
f1=0.01;
x=sin(2*pi*f1*t);

The above piece of code is just to generate filter's input.

You can just replace x with your audio signal

[hanif omar]

if x is input.can i put x is analogread ?