JNTU
JNTU B.Tech III SIGNALS AND SYSTEMS Previous Question Paper (August/September - 2021 - R18)
Answer any five questions. All questions carry equal marks.
Main
Find the expression for mean square error using the expression of a function using orthogonal signal space.
Answer
In orthogonal signal space, a signal x(t) can be approximated by a set of orthonormal basis functions {φn(t)} as x̂(t) = Σ cnφn(t). The error signal is defined as e(t) = x(t) - x̂(t). The mean square error (MSE) is the average power of the error signal, given by E = ∫ |e(t)|2 dt over the interval.
Substituting the expression for e(t):
Expanding the integral and utilizing the property of orthogonality (∫ φn(t)φm*(t) dt = 1 for n=m and 0 for n≠m), the cross-terms vanish. The expression simplifies to:
This result, known as Parseval's theorem for signal space, shows that the mean square error is minimized when the coefficients cn are chosen as the projections of x(t) onto the basis functions, specifically cn = ∫ x(t)φn*(t) dt.
Find the even and odd components of the signal
Answer
Given the signal x(t) = cos(t) + sin(t) + cos(t)sin(t), we use the definitions xe(t) = 0.5[x(t) + x(-t)] and xo(t) = 0.5[x(t) - x(-t)].
First, find x(-t):
Now, calculate the even component:
Next, calculate the odd component:
Derive the expression for component vector of approximating the function
Answer
Sign in to view the complete answer paper.
Define and sketch the following elementary signals: i) Exponential Signals ii) Sinusoidal Signals
Answer
Sign in to view the complete answer paper.
Explain Dirichlet’s conditions to obtain Fourier series representation of any signal.
Answer
Sign in to view the complete answer paper.
Obtain the relations between the coefficients of trigonometric Fourier series and Exponential Fourier series.
Answer
Sign in to view the complete answer paper.
Find the Fourier series representation and sketch the amplitude and phase spectrum for the signal
Answer
Sign in to view the complete answer paper.
With regard to Fourier series representation, justify the following statements: i) Odd functions have only sine term ii) Even functions have no sine term iii) Functions with half wave symmetry have only odd harmonics.
Answer
Sign in to view the complete answer paper.
Find the convolution using graphical method of the following two signals:
Answer
Sign in to view the complete answer paper.
Explain causality and physical reliability of a system and explain Paley-Wiener criterion.
Answer
Sign in to view the complete answer paper.
Obtain the relationship between the bandwidth and rise time of ideal High pass filter.
Answer
Sign in to view the complete answer paper.
Find the inverse z-transform of
Answer
Sign in to view the complete answer paper.
State and Prove sampling theorem for low pass signals. Also, explain the recovery of original signal from its sampled signal. Draw neat diagrams wherever necessary.
Answer
Sign in to view the complete answer paper.
List and explain the properties of Auto-correlation.
Answer
Sign in to view the complete answer paper.