Test: Frequency Selective Filters - Electronics and Communication Engineering (ECE) MCQ

Explanation: The given impulse response is h(n)=Asin(n+1)ω₀u(n).
According to the above equation, the second order system with complex conjugate poles on the unit circle is a sinusoid and the system is called a digital sinusoidal oscillator or a Digital frequency synthesizer.

Explanation: The system with the system function given as H(z)=z -k is a pure delay system . It has a constant gain for all frequencies and hence called as All pass filter.

Explanation: A comb filter can be viewed as a notch filter in which the nulls occur periodically across the frequency band, hence the analogy to an ordinary comb that has periodically spaced teeth.

Explanation: The given figure represents the frequency response characteristic of a notch filter with nulls at frequencies at ω0 and ω1.

Explanation: The magnitude response of a band pass filter with two complex poles located near the unit circle is as shown below.

The filter gas a large magnitude response at the poles and hence it is called as digital resonator.

Explanation: The difference equation for the high pass filter is
y(n)=-0.9y(n-1)+0.1x(n)
and its frequency response is given as
H(ω)= 0.1/(1+0.9e^-jω).

Explanation: The impulse response of a high pass filter is simply obtained from the impulse response of the low pass filter by changing the signs of the odd numbered samples in h_lp(n). Thus
h_hp(n)=(-1)_n h_lp(n)=(e^jπ)ⁿ h_lp(n)
Thus the frequency response of the high pass filter is obtained as H_lp(ω-π).

Explanation: Clearly, the filter must have poles at P_1,2=re^±jπ/2 and zeros at z=1 and z=-1. Consequently the system function is

Explanation: We know that the group delay of the system with phase ϴ(ω) is defined as
T_g(ω)=(dϴ(ω))/dω
Given the phase is linear=> the group delay of the system is constant.

Explanation: For an ideal filter, in the magnitude response plot at the stop band it should have a sudden fall which means an ideal filter should have a zero gain at stop band.