Hi, everyone, welcome to this lecture.
In this lecture, we will learn why digital freedoms are important.
Why do we design digital filters?
What are the requirements the with this?
So basically, digital filters serve two important purposes.
And does this signal separation and signal restoration?
Now, what is signal separation and signals extradition must signal separation is that if two are effectively
separable, then we can design a digital filter to separate them.
Spectral separable means that they have different frequency.
Concord's it means that if we have two segments and we want to separate them, so we have to be fully
across some of the segments.
And if they have a separate frequency component, then they can be separate by Freeda, for instance.
These are the two in infrequency me and we can see that the regular segment is different or is looking
separate from the green color.
So if we see the frequency value at 20 hertz, these signals are separable.
So there is no overlapping between the signal after 20 years.
So we can easily separate this signal from the green signal.
But if we want to retain the right signal and we want to figure out the green, that we have to design
a low battery because these values are at the lower frequency.
And you can see that these values are between zero and 20.
Similarly, if we want to retain this green signal and we want to filter out this red, we have to design
a hypothesis which cut off frequency maybe 20 years so we can see that we can simply separate these
two sigma because these two signals are actually separable.
That is the acceptable in terms of their frequencies.
Now, there might be the possibility that this red color may overlap this green color to the few instances
of the frequencies that is between 20 and 30.
In that case, it is difficult to separate for that part of the frequency where the frequency contents
are mixed.
But if they are different from each other, they can be easily separated by designing a suitable low
for the hyperspeed.
So this is called the signal separation.
That is, you have to design a suitable distance to separate these two signals.
The other purpose of digital design is signal restoration.
If a signal is corrupted by noise, then we can restore or recover or lose the signal by presenting
a data that with proper characteristic depending upon the type of noise kind of privacy not.
It means we have a noisy signal and we want to recover our original signal.
So we have to separate the noise or you have to filter the noise from the signal.
So in this case, we have to design a proper filter that can that can restore our signal by eliminating
the noise.
So that is the second important requirement from the little filter, which is signal restoration or
signal recovery.
Now, this is an example of the kind of activity you can see that now this red signal is a band possibly.
So here we have used the band by speaker signals.
We will discuss the Lobos bypass band and band staff later in detail in this section.
It's just an example of signal restoration that this green signal is a signal plus noise.
And now we have recovered a little red signal by band by splitting the green signal.
So in this case, you can see that this red signal is properly recovered from this signal.
So this is second important application for the purpose of designing digital 3D.
Now, the digital filters has to be based upon the impulse response.
What is the meaning of impulse response?
No response means output and impulse is the signal which we have discussed in Section three of this
post, not impulse response means if you give impulse signal to the input of the filter.
So if this response is finite, then that there is a finite impulse response to that.
And if the response is infinite, actually that is infinite impulse response.
Now what does it mean is finite impulse response and finite impulses?
So our finite impulses must be that is a signal processing filter or a digital filter whose impulse
response to any final input signal is of finite duration.
This is because it can lead this to zero in a short time and thus it is best to.
So if we give suitable input to a filter and it can work this to zero in a short period of time, and
actually that is called a finite impulse response.
And the reason of this convergence is that it is a stable vector.
In contrast, to find out whether there is an infinite impulse response to the infinite impulse response
filter does not and left this to zero over a finite interval of time because it is an estimate.
So so that reason of a the idea of freedom is their characteristic.
So basically it can leave this to zero because finite impulse response with it somehow depends upon
the convolution.
And we have studied convolution in Section four of this code.
So you find that impulse responsible.
Does working somehow depends upon the convolution, which is a finite duration process?
On the other hand, the working of infinite impulse responsibilities depends upon reCAPTCHA.
So we will discuss detail in detail, the infinite impulse, response and recursion in the next section
of the post.
So basically this section is for finite impulse response system.
So finite impulse response system is stable and the first reason was that it's dependent upon the convolution.
The other reason is that this will depend upon the present value of the signal that it is less dependent
on the signal.
It means that during the 50 Cent process, its separation or its working depends only upon the present
value of the signal.
On the other hand, infinite in response is unstable because its working depends upon the present value
of the signal and also the possibility of the signal to duplicate it in the infinite.
In response to that, it's working depends upon the present and the value of the signal of signal.
So this finite impulse response to that is less dependent.
Therefore it is stable and it can live this to zero and gives finite impulses and infinite impulse response
basically depend upon the data that is depend upon the present and the value of the data.
Therefore, it remains and is stable and it takes long on approximately infinite length of time to converge
to zero.
So this was the introduction of the reasons why they were designed.
What are the words from that filter?
What are there according to the impulse response?
That is that if an athlete knows when this section totally belongs to FISA.
So in this section, we will learn how we can design different FISA to serve the purpose of signal processing.
And in the next section, we will learn in detail about the infinite impulse response and then designing
evolution and then implementation.
So in the next video, we will learn and we will see what are the important steps in designing of finite
inputs.
Response once the.