It gives the basic introduction about the Discrete Filters.

1. Group Discussion
PHM501

2. Filtering-Discrete Filters-Recursive
•Filtering- It is a class of signal processing, the
defining features of filters being the
complete or partial suppression of some aspect of the
signal. Most often, this means removing some
frequencies or frequency bands.
•Filters- A filter is a circuit capable of passing
(or amplifying) certain frequencies while
attenuating other frequencies. Thus, a filter can
extract important frequencies from signals that also
contain undesirable or irrelevant frequencies.

3. In the field of electronics, there are many applications for filters.
Examples include:
Radio Communications: Filters enable radio receivers
to only “see” the desired signal while
rejecting all other signals (assuming that the other signals have
different frequency content.
DC power supplies: Filters are used to eliminate undesired high
frequencies(i.e., noise) that are present on
AC input lines. Additionally, filters are used on a power supply’s
output to reduce ripples.
Audio Electronics: A crossover network is a network of filters
to channel low-frequency audio to woofers,
mid range frequencies to midrange speakers, and high-
frequencies sounds to tweeters.

4. Four major types of Filters:
1. Low-pass filter
2. High-pass filter
3. Band-pass filter
4. Notch filter
Discrete Time Filters-
Discrete time filters are describes by the difference equations:
•Recursive Filters: Impulse Response of infinite length
(IIR Systems)
•Non- Recursive Filters: Impulse response of finite Length
(FIR Systems)

5. Recursive Discrete Time Filters:
First Order Difference Equation:
D

6. Recursive Discrete Time Filters:
Simple Recursive Difference equation can act as low pass or high
pass filter,
The corresponding frequency response is,

7. On taking Fourier Transform of the above difference equation,
⇒
F