Response of a Ltic System Time-Domain Analysis
Circuits & Signals
EEE/ INSTR C272
BITS Pilani
Pilani Campus p
ANU GUPTA EEE
Time-domain analysis
BITS Pilani
Pilani Campus p
Response of a LTIC system time-domain analysis linear, time-invariant, continuous-time (LTIC) systems--Total response = zero-input response + zero-state response zero-input response component that results only from the initial i t t th t lt l f th i iti l conditions at t = 0 with the input f(t) = 0 for t ≥ 0, zero-state zero state response component that results only from the input f(t) or t ≥ 0 when the initial conditions (at t = 0) are assumed to be zero. decomposition property. The system output is zero when the input is zero only if the system is in zero state. Zero state, meaning the absence of all internal energy g ; , storages; that is, all initial conditions are zero.
BITS Pilani, Pilani Campus
LTIC System C. C T
BITS Pilani, Pilani Campus
Differentiator increases noise Why?
The derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity Derivative of a fluctuating signal has more fluctuations then the signal itself . As it shows change in a small interval Δt. A steep change causes derivative to show large peaks graphically
Thus if noise ( random signal) in a signal is getting differentiated along with the signal then resultant signal has more noise signal,
BITS Pilani, Pilani Campus
Differentiation of a signal has the reputation for being a noisy operation. Even if the signal is band-limited, noise will introduce high frequency signals which are greatly amplified by differentiation. p y Thus in a differentiator , high-frequency noise signals will not be suppressed by this circuit; rather they will be amplified f b lifi d far beyond th amplification of th d i d signal d the lifi ti f the desired i l Thus to smoothen out the signal filters are used
EEE/ INSTR C272
BITS Pilani
Pilani Campus p
ANU GUPTA EEE
Time-domain analysis
BITS Pilani
Pilani Campus p
Response of a LTIC system time-domain analysis linear, time-invariant, continuous-time (LTIC) systems--Total response = zero-input response + zero-state response zero-input response component that results only from the initial i t t th t lt l f th i iti l conditions at t = 0 with the input f(t) = 0 for t ≥ 0, zero-state zero state response component that results only from the input f(t) or t ≥ 0 when the initial conditions (at t = 0) are assumed to be zero. decomposition property. The system output is zero when the input is zero only if the system is in zero state. Zero state, meaning the absence of all internal energy g ; , storages; that is, all initial conditions are zero.
BITS Pilani, Pilani Campus
LTIC System C. C T
BITS Pilani, Pilani Campus
Differentiator increases noise Why?
The derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity Derivative of a fluctuating signal has more fluctuations then the signal itself . As it shows change in a small interval Δt. A steep change causes derivative to show large peaks graphically
Thus if noise ( random signal) in a signal is getting differentiated along with the signal then resultant signal has more noise signal,
BITS Pilani, Pilani Campus
Differentiation of a signal has the reputation for being a noisy operation. Even if the signal is band-limited, noise will introduce high frequency signals which are greatly amplified by differentiation. p y Thus in a differentiator , high-frequency noise signals will not be suppressed by this circuit; rather they will be amplified f b lifi d far beyond th amplification of th d i d signal d the lifi ti f the desired i l Thus to smoothen out the signal filters are used