Unaltered signal

Time domain:

Frequency domain:

Butter worth Filter:

Specifications:

I used Butter worth filter of following specification:

Type: Band pass

Order: 2

Start Frequency: 100 Hz

Stop Frequency: 300 Hz

These frequencies are normalized with Fs/2 so that can between 0 and 1. i-e:

Start Frequency: 100/ (Fs/2) = 100/ (48000/2) = 0.00467 Hz

Stop Frequency: 300/ (Fs/2) = 300/ (48000/2) = 0.00625 Hz

I choose these set of frequencies to minimize the high frequency noise which is starting above 1100 Hz. Our desired signal is below 1000 Hz (Human voice) which we want to extract. I started by choosing different set of frequencies such as 

Start freq : 100 Hz , Stop freq : 900Hz Start freq : 100 Hz , Stop freq : 800Hz

Start freq : 100 Hz , Stop freq : 700Hz Start freq : 100 Hz , Stop freq : 600Hz

Start freq : 100 Hz , Stop freq : 500Hz And got the best noise reduction at : Start freq : 100 Hz , Stop freq : 300Hz So I selected these frequencies.

Transfer function:

  0.0001682 - 0.0003364 z^-2 + 0.0001682 z^-4

  ------------------------------------------------------------------------

  1 - 3.962 z^-1 + 5.888 z^-2 - 3.889 z^-3 + 0.9637 z^-4 

Frequency Response of Butter worth filter: 

Filtered Signal:

Time Domain: 

Frequency Domain:

Comparison:

The transition (cut off region) of Butterworth filter is not as sharp as in the case of FIR filters so high frequencies are not decreased completely as shown in the figure, so to completely get rid of these frequencies and cutting human voice signal I used a low pass FIR filter of cut off frequency 1100 Hz on the output of Butterworth filter. 

Visual Comparison:

Original signal

After applying Butter worth Filter:

After applying low pass FIR Filter:

Hidden Message:

“Forgive me if don’t shake hand.” Tombstone