It contains the introduction of Low Pass Filter and classification of the same in Signals & Systems point of view. It is a brief presentation done by me as a case study of L.P.F. in college.

1. Low Pass Filter
SIES Grad. School of Tech : S.E. – EXTC A-3
Atharva Karnik (117A2048)

2. What is a Low Pass Filter ?
• A circuit arrangement which allows signals of frequencies ranging
from 0 Hz to fH Hz (fH = higher cut-off frequency)
• Signals of frequencies greater than fH Hz are rejected
• Consists of one resistive (Resistor) and one reactive (Capacitor)
component
• High attenuation is offered at frequencies beyond fH Hz

3. RC Low Pass Filter
• Simplest L.P.F. consists of 1 Resistor and 1 Capacitor. In this type of
arrangement, input (Vin) is applied to series combination of resistor
(R) and capacitor (C) but the output signal (Vout) is taken across
capacitor only.

4. Transfer Function of 1st order LPF
By transforming the circuit into frequency domain, we get the transfer function of
L.P.F. as follows. Thus, when frequency increases, transfer function decreases.

5. Classification of LPF as System
• As it doesn’t have any active elements, LPF is Linearly Time Invariant
system
• Ideally LPF should be non-causal. But practically it is Causal system
• Ideally LPF should be unstable due to charge storing capability of
capacitor. But in practice, it is Stable system
• It is a Static system as capacitor doesn’t have any discharge path
• It is neither Inversible nor Non-inversible system as only low frequency
components can be recovered from output while high frequency
components are lost in the form of heat energy.

6. Classification of LPF Signals
• Periodicity of output signal is dependent upon application.
• Practically it is neither Even nor Odd as such signals don’t exist.
• Neither Deterministic nor Non-Deterministic as it depends upon the
input signal applied to the system.
• Practically output is always Power signal as it remains finite even at
infinite values of time.
• Basically, LPF passes every signal which has lower frequency than fc.
Thus, signal properties depend upon only the values of components
used for addition of noise and thus affecting signal quality.

7. Applications of Low Pass Filters
• Audio applications such as passing signals which have audio frequency only
• Signal processing in equalizers where operations are needed to be
performed on specific frequency signals
• Reception of baseband signals in superheterodyne receivers e.g. GMRT
telescopes
• Anti-aliasing filter in Image Processing
• Used as Integrator in few applications
• Telephone system uses LPF to convert audio frequencies of speaker to a
band limited 0.3 KHz to 3.4 KHz Voice Band Signal

8. References
• http://www.etti.unibw.de/labalive/experiment/lti/
• https://en.wikipedia.org/wiki/Low-pass_filter
• https://nptel.ac.in/courses/117101055/group10/grp10/sas_10/pa
ge06_8_3_2004.php
• https://www.electronicshub.org/active-low-pass-filter/
• https://www.electronics-tutorials.ws/filter/filter_2.html
• Images are taken from the above sites

9. Thank You !!