7. A finite pulse train waveform is composed of 20 pulses, each of 10 µs length and separated by a PRI of 1 ms. What is the coherent processing interval for this waveform? What is the peak-to-null Doppler resolution? 8. For the pulse train waveform of problem 7, sketch the spectrum in a form similar to Figure 8-6. Indicate the Rayleigh width and the spacing of the individual spectral lines. How many indi- vidual spectral lines fall within the main lobe of the sinc-shaped envelope determined by the pulse length? FIGURE 8-6 . Finite pulse train signal and its spectrum. Pr(0) -2T -T T 27 ArT/T PRF -1/r 1/r 2/r
7. A finite pulse train waveform is composed of 20 pulses, each of 10 µs length and separated by a PRI of 1 ms. What is the coherent processing interval for this waveform? What is the peak-to-null Doppler resolution? 8. For the pulse train waveform of problem 7, sketch the spectrum in a form similar to Figure 8-6. Indicate the Rayleigh width and the spacing of the individual spectral lines. How many indi- vidual spectral lines fall within the main lobe of the sinc-shaped envelope determined by the pulse length? FIGURE 8-6 . Finite pulse train signal and its spectrum. Pr(0) -2T -T T 27 ArT/T PRF -1/r 1/r 2/r
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Please I need a solution to problem 8 only. Thanks!
![### Problem 7:
A finite pulse train waveform is composed of 20 pulses, each of 10 µs length and separated by a PRI of 1 ms. What is the coherent processing interval for this waveform? What is the peak-to-null Doppler resolution?
### Problem 8:
For the pulse train waveform of problem 7, sketch the spectrum in a form similar to Figure 8-6. Indicate the Rayleigh width and the spacing of the individual spectral lines. How many individual spectral lines fall within the main lobe of the sinc-shaped envelope determined by the pulse length?
#### Explanation of Figure 8-6:
The figure illustrates a finite pulse train signal and its spectrum.
**Top Part - Time Domain Representation (pₜ(t)):**
- The pulse train consists of rectangular pulses.
- The horizontal axis represents time, denoted as \(t\), ranging from \(-2T\) to \(2T\).
- The length of each pulse is indicated by \(\tau\).
- The width of the entire pulse train is denoted as \(T_d\).
- \[P_F(t)\] represents the height of each pulse, denoted as \(A\).
**Bottom Part - Frequency Domain Representation (|P_F(f)|):**
- \(|P_F(f)|\) shows the spectral magnitude of the pulse train.
- The spectrum includes a series of spikes, representing the discrete spectral lines.
- The dashed envelope surrounding these spikes forms a sinc-shaped envelope, characteristic of the Fourier transform of a rectangular pulse train.
- The horizontal axis represents frequency, denoted as \(f\), with major points marked as \(-2/\tau\), \(-1/\tau\), 0, \(1/\tau\), and \(2/\tau\).
- The Rayleigh width (PRF) and individual spectral lines are marked. The primary spectral component is centered at \(0\) Hz.
This diagram helps in visualizing the relationship between the time-domain representation of the pulse train and its corresponding frequency-domain spectrum, important for understanding concepts like Doppler resolution and spectral line spacing in radar and communication systems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d1aa45e-af7c-45aa-98db-d49bc68e25fe%2F6c87d4ce-fb9f-47a9-bdac-4e046d1ff8cf%2Fe0f3rhe_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 7:
A finite pulse train waveform is composed of 20 pulses, each of 10 µs length and separated by a PRI of 1 ms. What is the coherent processing interval for this waveform? What is the peak-to-null Doppler resolution?
### Problem 8:
For the pulse train waveform of problem 7, sketch the spectrum in a form similar to Figure 8-6. Indicate the Rayleigh width and the spacing of the individual spectral lines. How many individual spectral lines fall within the main lobe of the sinc-shaped envelope determined by the pulse length?
#### Explanation of Figure 8-6:
The figure illustrates a finite pulse train signal and its spectrum.
**Top Part - Time Domain Representation (pₜ(t)):**
- The pulse train consists of rectangular pulses.
- The horizontal axis represents time, denoted as \(t\), ranging from \(-2T\) to \(2T\).
- The length of each pulse is indicated by \(\tau\).
- The width of the entire pulse train is denoted as \(T_d\).
- \[P_F(t)\] represents the height of each pulse, denoted as \(A\).
**Bottom Part - Frequency Domain Representation (|P_F(f)|):**
- \(|P_F(f)|\) shows the spectral magnitude of the pulse train.
- The spectrum includes a series of spikes, representing the discrete spectral lines.
- The dashed envelope surrounding these spikes forms a sinc-shaped envelope, characteristic of the Fourier transform of a rectangular pulse train.
- The horizontal axis represents frequency, denoted as \(f\), with major points marked as \(-2/\tau\), \(-1/\tau\), 0, \(1/\tau\), and \(2/\tau\).
- The Rayleigh width (PRF) and individual spectral lines are marked. The primary spectral component is centered at \(0\) Hz.
This diagram helps in visualizing the relationship between the time-domain representation of the pulse train and its corresponding frequency-domain spectrum, important for understanding concepts like Doppler resolution and spectral line spacing in radar and communication systems.
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