## Introduction to Bandpass Filter Matlab

Band Pass Filters are used to filter or isolate certain frequencies that lie in a particular range. These filters find their use in applications like audio amplifiers or circuits used in loudspeakers (crossover filters) or tone controls used in pre-amplifiers. In these applications, it is required to pass only a specific range of frequencies which don’t start at DC (0HZ) or they end at a higher frequency point but lie within a specific range, which can be either wide or narrow.

**Syntax:**

`F = bandpass (s, wp)`

`F = bandpass (s, fp, Fx)`

**Description:**

- F = bandpass(s, wp) is used to filter the signal ‘s’ with passband frequency range provided by the 2-element vector ‘wp’. If input ‘s’ is a matrix, the bandpass function will filter each column of ‘s’ independently
- F = bandpass (s, fp, Fx) is used to specify that the signal ‘s’ is sampled at a rate ‘Fx’ HZ. The 2-element vector ‘fp’ gives the passband frequency

### Examples of Bandpass Filter Matlab

Let us now understand the code of ‘Bandpass filter’ in MATLAB with the help of various examples:

#### Example #1

In this example, we will create a sine signal which is sampled at 10000Hz for 1 second and will pass it through a Bandpass filter.

Below are the steps to be followed:

- Define the sampling rate.
- Define the tones for the signal.
- Keep low frequency and high frequency tone at a level of three times the intermediate tone.
- Pass the above signal through the bandpass filter by setting the allowed frequencies.

**Code:**

`Fx = 1e4`

T = 0:1/Fx:1

`s = [3 1 3]*sin(pi*[50 100 300]'.*T) + randn(size(T))/20;`

`bandpass(s, [100 200], Fx)`

**Input:**

`Fx = 1e4`

T = 0:1/Fx:1

s = [3 1 3]*sin(pi*[50 100 300]'.*T) + randn(size(T))/20;

bandpass(s, [100 200], Fx)

**Output:**

As we can see in the output, we have obtained the original & filtered signals along with their spectra. The Bandpass filter has removed the frequencies below the low pass frequency and frequencies above the high pass frequency.

#### Example #2

In this example, we will create a cos signal which is sampled at 10000Hz for 1 second and will pass it through a Bandpass filter.

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Below are the steps to be followed:

- Define the sampling rate.
- Define the tones for the signal.
- Keep low frequency and high-frequency tone at a level of two times the intermediate tone.
- Pass the above signal through the bandpass filter by setting the allowed frequencies.

**Code:**

`Fx = 1e4`

T = 0:1/Fx:1

`s = [2 1 2]*cos(pi*[150 200 300]'.*T) + randn(size(T))/20;`

`bandpass(s, [100 200], Fx)`

**Input:**

`Fx = 1e4`

T = 0:1/Fx:1

s = [2 1 2]*cos(pi*[150 200 300]'.*T) + randn(size(T))/20;

bandpass(s, [100 200], Fx)

**Output****:**

As we can see in the output, we have obtained the original & filtered signals for our input cos signal along with their spectra. The Bandpass filter has removed the frequencies below the low pass frequency and frequencies above the high pass frequency.

#### Example #3

In the above 2 examples, we used a three-channel signal, in this example, we will use a 2-channel signal and will pass it through a Bandpass filter.

Below are the steps to be followed:

- Define the sampling rate.
- Define the tones for the signal.
- Keep high frequency twice the low frequency.
- Pass the above signal through the bandpass filter by setting the allowed frequencies.

**Code:**

`Fx = 1e4`

T = 0:1/Fx:1

`s = [2 1].*cos(2*pi*(0:64)'./[32 64])`

`bandpass(s, [100 200], Fx)`

**Input:**

`Fx = 1e4`

T = 0:1/Fx:1

s = [2 1].*cos(2*pi*(0:64)'./[32 64])

bandpass(s, [100 200], Fx)

**Output:**

As we can see in the output, we have obtained the original & filtered signals for our input cos signal along with their spectra. The Bandpass filter has removed the frequencies below the low pass frequency and frequencies above the high pass frequency.

### Conclusion

- Bandpass filters are used to get the frequencies that lie in a particular range.
- We use the Bandpass function in MATLAB to execute a Bandpass filter.
- The Bandpass function in MATLAB provides both original and filtered signals as output.
- This function also provides the spectra of the signals in the output.

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