Question:
A digital filter with impulse response $ h[n] = 2^n u[n] $ will have a transfer function with a region of convergence.
A digital filter with impulse response $ h[n] = 2^n u[n] $ will have a transfer function with a region of convergence.
Show Hint
The region of convergence (ROC) of a z-transform determines the stability and causality of a system. For a causal system, the ROC is outside a circle in the z-plane.
Updated On: Apr 11, 2025
- includes unit circle
- excludes unit circle
- bounded by rings with circles of radius 0.5 and 2
- entire z-plane excluding origin and infinity
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The given impulse response is \( h[n]=2^nu[n] \) which is a right sided sequence.
The z transform of \( a^n u[n] \) is given by \( \frac{1}{1-az^{-1}} \). Here \( a = 2 \)
Therefore, \(H(z) = \frac{1}{1-2z^{-1}}\) or \( H(z) = \frac{z}{z-2} \). For the sequence to be stable the ROC (region of convergence) must be outside the circle with radius 2. Therefore, it excludes the unit circle.
Was this answer helpful?
0
0
Top TANCET Electronics and Communication Engineering Questions
- Transfer characteristics of JFET is drawn between
- _______ capacitance affects high frequency response of CE amplifier.
- Forward current of 75mA passes through a diode for a forward drop of 0.6V. Find the forward resistance of the diode.
- Early effect in bipolar transistor is caused by
- Find the operating region of N-channel MOSFET with VGS = 1.4V, VTN = 0.5V, VDS = 1.8V
View More Questions
Top TANCET Digital Signal Processing Questions
- If the data rate of delta modulator output is 43.2 kbps, for the input signal of 3.6 kHz, then the sampling rate used is equal to,
Which of the following causal analog transfer functions is used to design causal IIR digital filter with transfer function? $$ H(z) = \frac{0.05z}{z-e^{-0.42}} + \frac{0.05z}{z-e^{-0.2}} $$ Assume impulse invariance transformation with \( T = 0.1 \, \text{s} \).
- The shape of the rectangular window function is changed to other function such as Hamming and Blackman window functions so that
- Window function used in FIR realization,
- The new pole locations due to truncation of coefficient to 4 bit including sign bit in the cascade realization \[ H(z) = \frac{1}{(1-0.95z^{-1})(1-0.25z^{-1})} \]
View More Questions
Top TANCET Questions
- If \( A \) is a \( 3 \times 3 \) matrix and the determinant of \( A \) is 6, then find the value of the determinant of the matrix \( (2A)^{-1} \):
- If the system of equations: \[ 3x + 2y + z = 0, \quad x + 4y + z = 0, \quad 2x + y + 4z = 0 \] is given, then:
- Let \[ M = \begin{bmatrix} 1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix} \] The maximum number of linearly independent eigenvectors of \( M \) is:
- The shortest and longest distance from the point \( (1,2,-1) \) to the sphere \( x^2 + y^2 + z^2 = 24 \) is:
- The solution of the given ordinary differential equation \( x \frac{d^2 y}{dx^2} + \frac{dy}{dx} = 0 \) is:
View More Questions