PPT on fourier transform application

1. Yashswasat Miital
SC19B126
Avionics
FourierTransform
Application
(Removal of noise from audio signals)

2. • In signal processing, noise is a general term for
unwanted (and, in general, unknown) modifications that
a signal may suffer during capture, storage,
transmission, processing, or conversion.
• Sometimes the word is also used to mean signals that are
random (unpredictable) and carry no useful information;
even if they are not interfering with other signals or may
have been introduced intentionally, as in comfort noise.
• Noise reduction, the recovery of the original signal from
the noise-corrupted one, is a very common goal in the
design of signal processing systems, especially filters.
Noise

3. Let there be an audio signal which contains two frequencies 400 Hz
and 4000 Hz.
Removal of Noise- An example

4. Consider a sinusoidal signal,
x(t) = sin(ωt)
Let the signal be affected by some noise,
x(t)measured = sin(ωt) + noise
Now take FourierTransform of x(t)measured ,
Now by setting the value of Xfiltered(ω) = 0 for frequencies above and below
required ω, the noise can be eliminated or reduced
Taking inverse FourierTransform of Xfiltered(ω) to get back x(t)filtered
How to apply FourierTransform:

5. Now, applying the FourierTransform to this signal which is
in time domain and obtaining it’s frequency spectrum:
400 Hz
4000 Hz

6. Setting the power of the frequencies other than 400 and -
400 Hz to be zero, we get the plot:

7. Applying the Inverse FourierTransform:

8. • Using Fourier Transform technique, we significantly
reduced noise from source signal.
• We observed that when we measured a signal
corrupted with noise has unwanted overshoots and
undershoots.
• After filtering process, we observed an uncorrupted
sinusoidal wave at output. No such information is lost
during the filtering process using Fourier Transform
technique.
• This method is also useful in Frequency Division
Multiplexing (FDM), where we have same frequency but
to avoid interference we superimpose different carrier
frequency on our source signal.
Inference:

9. Thank You