DFT and IDFT Matlab Code
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This document describes an experiment to perform the discrete Fourier transform (DFT) and inverse discrete Fourier transform (IDFT) on two input signals using MATLAB. The experiment calculates the magnitude and phase of the DFT and IDFT outputs and compares the results to the MATLAB FFT and IFFT functions. The student learns how to implement the DFT and IDFT and plot the magnitude and phase of signals.
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![ECE324: DIGITAL SIGNAL PROCESSING LABORATORY
Practical No.:4
Roll No: B-54 Registration No.:11205816_ Name:Shyamveer Singh
Aim: To perform DFT and IDFT of two given signals, Plot the
Magnitude and phase of same.
Mathematical Expressions Required:
1. DFT
2. IDFT
Inputs :
X(n)=[1 2 3 4 5]
X(k)=[2 4 6 8 9]
Program Codes:
1. DFT
function[y]=shyamdft(x)
m=length(x);
xk=zeros(1,m);
for k=0:m-1;
for n=0:m-1;
xk(k+1)=xk(k+1)+x(n+1)*exp((-i)*2*pi*k*n/m);
end
end
y=xk
M=sqrt(real(y).^2+imag(y).^2)
M1=abs(y)
A = atan2(imag(y),real(y))
A1=angle(y)
z=fft(x)
2. IDFT
function[y]=shyamidft(x)
m=length(x);
xk=zeros(1,m);
for k=0:m-1;
for n=0:m-1;
xk(k+1)=xk(k+1)+(1/m)*x(n+1)*exp((i)*2*pi*k*n/m)
;
end
end
y=xk
M=sqrt(real(y).^2+imag(y).^2)
M1=abs(y)
A = atan2(imag(y),real(y))
A1=angle(y)
z=ifft(x)
Outputs/ Graphs/ Plots:](https://image.slidesharecdn.com/11205816124547b-54-150415060149-conversion-gate01/85/DFT-and-IDFT-Matlab-Code-1-320.jpg)
![>> x=[1 2 3 4 5]
x=
1
2
3
4
5
>> shyamdft(x)
y=
15.0000
- 3.4410i
M=
15.0000
M1 =
15.0000
A=
0
A1 =
0
z=
15.0000
- 3.4410i
-2.5000 + 3.4410i
-2.5000 + 0.8123i
-2.5000 - 0.8123i
-2.5000
2.1991
2.8274
-2.8274
-2.1991
2.1991
2.8274
-2.8274
-2.1991
4.2533
2.6287
2.6287
4.2533
4.2533
2.6287
2.6287
4.2533
-2.5000 + 3.4410i
-2.5000 + 0.8123i
-2.5000 - 0.8123i
-2.5000
Comparison with inbuilt functions: A= angle or phase, M=magnitude compare with
inbuilt commands abs, angle.
Y is output Compare with Z inbuilt command.
Outputs/ Graphs/ Plots:
2. IDFT
x=[2 4 6 8 9]
x=
2
4](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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Matlab source codes section | Download MATLAB source code freerce-codes
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#Import standard math functions from math import import .docx
#Import standard math functions
from math import *
import numpy as np
import matplotlib.pyplot as plt
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def nu(M,y):
return sqrt((y+1)/(y-1))*atan(sqrt((y-1)*(M**2-1)/(y+1)))-
atan(sqrt(M**2-1))
#Prandtl-Meyer Expansion angle for numeric extraction of Mach
number
def nu2(M,nu,y):
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atan(sqrt(M**2-1))-nu
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def nudif(M, y = 1.25):
return sqrt(M**2-1)/(M*(1+(y-1)*M**2/2))
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def Pstag(Pe,M,y):
return Pe*(1+(y-1)/2*M**2)**(y/(y-1))
#Stagnation pressure ratio across a shockwave with P01
calculated from Pstat and M.
def Pstagratio(M,P02,P1,y):
P01 = Pstag(P1,M,y)
f1 = 2/((y+1)*(y*M**2-(y-1)/2)**(1/(y-1)))
f2 = (((y+1)/2*M)**2/(1+(y-1)/2*M**2))**(y/(y-1))
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#Stagnation pressure ratio across a shockwave with P01
calculated from Pstat and M.
def Pstagshock(M,P1,y):#returns P02
P01 = Pstag(P1,M,y)
f1 = 2/((y+1)*(y*M**2-(y-1)/2)**(1/(y-1)))
f2 = (((y+1)/2*M)**2/(1+(y-1)/2*M**2))**(y/(y-1))
return f1*f2*P01
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pressure, gamma, and Mach.
def Pstatshock(P,M,y,theta):
beta = shockangle(M,y,theta)[1]
return P*(1+2*y/(y+1)*((M*sin(beta))**2-1))
#Numerical derivative for this particular function with only x
(which is M) varying.
def centraldiff(func, x, A, Ast, y, h = 0.0000001):
return (func(x+h,A,Ast,y)-func(x-h,A,Ast,y))/(2*h)
#Newton's method for four-term fuction.
def Newts(func, fin,y,A,Ast, err, iMax = 100000):
x1 = fin
it = 0
ea = np.Infinity
while ea > err and it < iMax:
x0 = x1
x1 = x0 - func(x0,A,Ast,y)/
(centraldiff(func,x0,A,Ast,y))
#x1 = x0 - func(x0,A,Ast,y)/(RPdif(x0,y))
it +=1
ea = abs((x0-x1)/x1)
return x1
#Newton's method
def Newt(Mguess,nu,gamma,err,iMax=1000):
x1 = Mguess
it = 0
ea = 100000
while ea > err and it < iMax:
x0 = x1
x1 = x0 - nu2(x0,nu,gamma)/nudif(x0,gamma)
it +=1
ea = abs((x0-x1)/x1)
return x1
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def Pexpand(M1, M2, P1, y):
top = 1+(y-1)/2*M1**2
bot = 1+(y-1)/2*M2**2
return P1*(top/bot)**(y/(y-1))
#Explicit solution for beta angle. Requires theta input in
degrees.
def shockangle(M,y,thd):
th = thd*pi/180
lt1 = (M**2-1)**2
lt2 = (1+(y-1)/2*M**2)
lt3 = (1+(y+1)/2*M**2)
l = (lt1-3*lt2*lt3*tan(th)**2)**.5
xt1 = (M**2-1)**3
xt2 = lt2
xt3 = (1+(y-1)/2*M**2+(y+1)/4*M**4)
x = (xt1-9*xt2*xt3*tan(th)**2)/l**3
tanb = []
for i in range(2):
tt1 = (M**2-1)
tt2 = 2*l*cos((4*pi*float(i)+acos(x))/3)
tt3 = 3*(1+(y-1)/2*M**2)*tan(th)
tanb.append((tt1+tt2)/tt3)
return (atan(tanb[0]),atan(tanb[1]))
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- 1. ECE324: DIGITAL SIGNAL PROCESSING LABORATORY Practical No.:4 Roll No: B-54 Registration No.:11205816_ Name:Shyamveer Singh Aim: To perform DFT and IDFT of two given signals, Plot the Magnitude and phase of same. Mathematical Expressions Required: 1. DFT 2. IDFT Inputs : X(n)=[1 2 3 4 5] X(k)=[2 4 6 8 9] Program Codes: 1. DFT function[y]=shyamdft(x) m=length(x); xk=zeros(1,m); for k=0:m-1; for n=0:m-1; xk(k+1)=xk(k+1)+x(n+1)*exp((-i)*2*pi*k*n/m); end end y=xk M=sqrt(real(y).^2+imag(y).^2) M1=abs(y) A = atan2(imag(y),real(y)) A1=angle(y) z=fft(x) 2. IDFT function[y]=shyamidft(x) m=length(x); xk=zeros(1,m); for k=0:m-1; for n=0:m-1; xk(k+1)=xk(k+1)+(1/m)*x(n+1)*exp((i)*2*pi*k*n/m) ; end end y=xk M=sqrt(real(y).^2+imag(y).^2) M1=abs(y) A = atan2(imag(y),real(y)) A1=angle(y) z=ifft(x) Outputs/ Graphs/ Plots:
- 2. >> x=[1 2 3 4 5] x= 1 2 3 4 5 >> shyamdft(x) y= 15.0000 - 3.4410i M= 15.0000 M1 = 15.0000 A= 0 A1 = 0 z= 15.0000 - 3.4410i -2.5000 + 3.4410i -2.5000 + 0.8123i -2.5000 - 0.8123i -2.5000 2.1991 2.8274 -2.8274 -2.1991 2.1991 2.8274 -2.8274 -2.1991 4.2533 2.6287 2.6287 4.2533 4.2533 2.6287 2.6287 4.2533 -2.5000 + 3.4410i -2.5000 + 0.8123i -2.5000 - 0.8123i -2.5000 Comparison with inbuilt functions: A= angle or phase, M=magnitude compare with inbuilt commands abs, angle. Y is output Compare with Z inbuilt command. Outputs/ Graphs/ Plots: 2. IDFT x=[2 4 6 8 9] x= 2 4
- 3. 6 8 9 >> shyamidft(x) y= 5.8000 + 1.1862i M= 5.8000 M1 = 5.8000 A= 0 A1 = 0 z= 5.8000-1.0618 - 1.1862i -0.8382 - 0.2074i -0.8382 + 0.2074i -1.0618 + 1.1862i Comparison with inbuilt functions:A= angle or phase, M=magnitude compare with inbuilt commands abs, angle. Y is output Compare with Z inbuilt command. -2.3009 -2.8991 2.8991 2.3009 -2.3009 -2.8991 2.8991 2.3009 1.5920 0.8635 0.8635 1.5920 1.5920 0.8635 0.8635 1.5920 -1.0618 - 1.1862i -0.8382 - 0.2074i -0.8382 + 0.2074i -1.0618 Analysis/ Learning outcomes: After performing this experiment we know about the DFT and IDFT implantation using MATLAB ,and we also know how to plot a phase and magnitude plot of a signal. Magnitude And Phase: Magnitude: M=sqrt(real(y).^2+imag(y).^2) Compare with inbuilt command abs. PHASE:A = atan2(imag(y),real(y)) Compare with inbuilt command angle.