A voice signal with a Bandwidth of 3 kHz is sampled at the Nyquist Rate and converted to a binary signal using 8 bits per sample. The Binary Signal is then encoded with Unipoplar NRZ as follows. mlt) 1 T, 27, 37, 4T, ST, 67, 77, This signal is used to modulate at carrier signal as follows. m(t) 10 cos(2m 100000 t) A. Sketch the spectrum of 4, (t). If the same binary signal is used to create a modulated signal according to the following formula: $2(t) = 10 cos[2r(95000 + 10000 m(t))t] B. Sketch the spectrum of 2(t).
A voice signal with a Bandwidth of 3 kHz is sampled at the Nyquist Rate and converted to a binary signal using 8 bits per sample. The Binary Signal is then encoded with Unipoplar NRZ as follows. mlt) 1 T, 27, 37, 4T, ST, 67, 77, This signal is used to modulate at carrier signal as follows. m(t) 10 cos(2m 100000 t) A. Sketch the spectrum of 4, (t). If the same binary signal is used to create a modulated signal according to the following formula: $2(t) = 10 cos[2r(95000 + 10000 m(t))t] B. Sketch the spectrum of 2(t).
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![### Modulation of a Binary Signal
#### Overview:
A voice signal with a bandwidth of 3 kHz is sampled at the Nyquist Rate and converted into a binary signal using 8 bits per sample. The binary signal is encoded with Unipolar Non-Return-to-Zero (NRZ) encoding.
#### Signal Representation:
The diagram shows the binary signal \( m(t) \) as a square wave. The x-axis represents time with segments labeled \(0, T_b, 2T_b, \ldots, 8T_b\), and the y-axis represents amplitude with values 0 and 1. This indicates a typical binary sequence over one period.
#### Modulation Process:
1. **Carrier Signal Modulation:**
- The binary signal \( m(t) \) is used to modulate a carrier signal, given by the equation
\[
\phi_1(t) = 10 \cos(2\pi \times 100000 \times t)
\]
2. **Diagram Description:**
- A block diagram shows \( m(t) \) modulating a carrier signal at frequency \( 100 \text{kHz} \) via multiplication, resulting in the modulated signal \( \phi_1(t) \).
#### Tasks:
**A. Sketch the Spectrum of \( \phi_1(t) \):**
When modulating a signal with a carrier frequency, the frequency spectrum of the modulated wave consists of two sidebands located symmetrically around the carrier frequency \(100 \text{kHz}\). Sketch the amplitude against frequency, illustrating a central spike at \( 100 \text{kHz}\) with sidebands influenced by the original binary signal bandwidth.
**B. Sketch the Spectrum of \( \phi_2(t) \):**
- If the same binary signal is used to create a modulated signal using the formula:
\[
\phi_2(t) = 10 \cos[2\pi(95000 + 10000 m(t))t]
\]
- The spectrum will again have sidebands, but these will now be centered around \( 95 \text{kHz} \) instead of \( 100 \text{kHz} \), reflecting the frequency deviation caused by the binary encoding.
In both cases, the sketches should illustrate the key frequencies and bandwidths, demonstrating the impact of NRZ-encoded binary modulation on carrier signals.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6508e563-9273-4604-9425-75422bfe07f7%2Fe3bc017a-fa2a-492c-a9af-e3ccb9838d93%2Fy9wmzo37_processed.png&w=3840&q=75)
Transcribed Image Text:### Modulation of a Binary Signal
#### Overview:
A voice signal with a bandwidth of 3 kHz is sampled at the Nyquist Rate and converted into a binary signal using 8 bits per sample. The binary signal is encoded with Unipolar Non-Return-to-Zero (NRZ) encoding.
#### Signal Representation:
The diagram shows the binary signal \( m(t) \) as a square wave. The x-axis represents time with segments labeled \(0, T_b, 2T_b, \ldots, 8T_b\), and the y-axis represents amplitude with values 0 and 1. This indicates a typical binary sequence over one period.
#### Modulation Process:
1. **Carrier Signal Modulation:**
- The binary signal \( m(t) \) is used to modulate a carrier signal, given by the equation
\[
\phi_1(t) = 10 \cos(2\pi \times 100000 \times t)
\]
2. **Diagram Description:**
- A block diagram shows \( m(t) \) modulating a carrier signal at frequency \( 100 \text{kHz} \) via multiplication, resulting in the modulated signal \( \phi_1(t) \).
#### Tasks:
**A. Sketch the Spectrum of \( \phi_1(t) \):**
When modulating a signal with a carrier frequency, the frequency spectrum of the modulated wave consists of two sidebands located symmetrically around the carrier frequency \(100 \text{kHz}\). Sketch the amplitude against frequency, illustrating a central spike at \( 100 \text{kHz}\) with sidebands influenced by the original binary signal bandwidth.
**B. Sketch the Spectrum of \( \phi_2(t) \):**
- If the same binary signal is used to create a modulated signal using the formula:
\[
\phi_2(t) = 10 \cos[2\pi(95000 + 10000 m(t))t]
\]
- The spectrum will again have sidebands, but these will now be centered around \( 95 \text{kHz} \) instead of \( 100 \text{kHz} \), reflecting the frequency deviation caused by the binary encoding.
In both cases, the sketches should illustrate the key frequencies and bandwidths, demonstrating the impact of NRZ-encoded binary modulation on carrier signals.
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