Digital Signal Processing Practice Test 10

1. The differential predictive signal quantizer system is known as?

None of the mentioned

DCPM

DPCM

DMPC

2. To reduce the dynamic range of the difference signal d(n) = x(n) - \(\hat{x}(n)\), thus a predictor of order p has the form?

\(\hat{x}(n)=\sum_{k=1}^pa_k x(n+k)\)

\(\hat{x}(n)=\sum_{k=1}^pa_k x(n-k)\)

\(\hat{x}(n)=\sum_{k=0}^pa_k x(n-k)\)

\(\hat{x}(n)=\sum_{k=0}^pa_k x(n+k)\)

3. According to the sampling theorem for low pass signals with T₁=1/B, then what is the expression for u_s(t) = ?

\(\sum_{m=-∞}^∞ u_s (mT_1-\frac{T_1}{2}) \frac{sin⁡(\frac{π}{T_1}) (t-mT_1-\frac{T_1}{2})}{(\frac{π}{T_1})(t-mT_1-\frac{T_1}{2})}\)

\(\sum_{m=-∞}^∞ u_s (mT_1-\frac{T_1}{2}) \frac{sin⁡(\frac{π}{T_1}) (t-mT_1+\frac{T_1}{2})}{(π/T_1)(t-mT_1+\frac{T_1}{2})}\)

\(\sum_{m=-∞}^∞ u_c (mT_1) \frac{sin⁡(\frac{π}{T_1}) (t+mT_1)}{(\frac{π}{T_1})(t+mT_1)}\)

\(\sum_{m=-∞}^∞ u_c (mT_1) \frac{sin⁡(\frac{π}{T_1}) (t-mT_1)}{(\frac{π}{T_1})(t-mT_1)}\)

4. What is the impulse response of an S/H, when viewed as a linear filter?

h(t)=\(\begin{cases}1,0<t≤T\\0,otherwise\end{cases}\)

None of the mentioned

h(t)=\(\begin{cases}1,0≤t≤T\\0,otherwise\end{cases}\)

h(t)=\(\begin{cases}1,0≥t≥T\\0,otherwise\end{cases}\)

5. Which low pass signal component occurs at the rate of B samples per second with odd numbered samples of x(t)?

u_c & u_s - lowpass signal component

u_c - lowpass signal component

u_s - lowpass signal component

none of the mentioned

6. If we substitute the equation \(x_l (t)= u_c (t)+j u_s (t)\) in equation x (t) + j ẋ (t) = x_l(t) e^j2πF_ct and equate real and imaginary parts on side, then what are the relations that we obtain?

x(t)=\(u_c (t) \,cos⁡2π \,F_c \,t+u_s (t) \,sin⁡2π \,F_c \,t\); ẋ(t)=\(u_s (t) \,cos⁡2π \,F_c \,t-u_c \,(t) \,sin⁡2π \,F_c \,t\)

x(t)=\(u_c (t) \,cos⁡2π \,F_c \,t-u_s (t) \,sin⁡2π \,F_c \,t\); ẋ(t)=\(u_s (t) \,cos⁡2π \,F_c t+u_c (t) \,sin⁡2π \,F_c \,t\)

x(t)=\(u_c (t) \,cos⁡2π \,F_c \,t-u_s (t) \,sin⁡2π \,F_c \,t\); ẋ(t)=\(u_s (t) \,cos⁡2π \,F_c \,t-u_c (t) \,sin⁡2π \,F_c \,t\)

x(t)=\(u_c (t) \,cos⁡2π \,F_c t+u_s (t) \,sin⁡2π \,F_c \,t\); ẋ(t)=\(u_s (t) \,cos⁡2π \,F_c t+u_c (t) \,sin⁡2π \,F_c \,t\)

7. There is no requirement to process the various signals at different rates commensurate with the corresponding bandwidths of the signals.

False

True

8. If a possible representation of a band pass signal is obtained by expressing x_l (t) as \(x_l (t)=a(t)e^{jθ(t})\) then what are the equations of a(t) and θ(t)?

a(t) = \(\sqrt{u_c^2 (t)-u_s^2 (t)}\) and θ(t)=\(tan^{-1}\frac{u_s (t)}{u_c (t)}\)

a(t) = \(\sqrt{u_c^2 (t)+u_s^2 (t)}\) and θ(t)=\(tan^{-1}\frac{u_c (t)}{u_s (t)}\)

a(t) = \(\sqrt{u_s^2 (t)-u_c^2 (t)}\) and θ(t)=\(tan^{-1}⁡\frac{u_s (t)}{u_c (t)}\)

a(t) = \(\sqrt{u_c^2 (t)+u_s^2 (t)}\) and θ(t)=\(tan^{-1}\frac{u_s (t)}{u_c (t)}\)

9. In the relation, x(t) = \(u_c (t) cos⁡2π \,F_c \,t-u_s (t) sin⁡2π \,F_c \,t\) the low frequency components u_c and u_s are called _____________ of the bandpass signal x(t).

Triplet components

None of the mentioned

Quadratic components

Quadrature components

10. The filter eliminates the spectrum of X(ω) in the range π/D < ω < π.

False

True