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Given a sequence x[n], to generate the sequence y[n] = x[3 – 4n], which one of the following procedures would be correct?
  • a)
    First delay x(n) by 3 samples to generate z1[n], then pick every 4th sample of z1[n] to generate z2[n], and than finally time reverse z2[n] to obtain y[n].
  • b)
    advance x[n] by 3 samples to generate z1[n], then pick every 4th sample of z1[n] to generate z2[n], and then finally time reverse z2[n] to obtain y[n]
  • c)
    First pick every fourth sample of x[n] to generate v1[n], time-reverse v1[n] to obtain v2[n], and then finally advance v2[n] by 3 samples to obtain y[n]
  • d)
    First pick every fourth sample of x[n] to generate v1[n], time-reverse v1[n] to obtain v2[n], and finally delay v2[n] by 3 samples to obtain y[n]
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Given a sequence x[n], to generate the sequence y[n] = x[3 – 4n]...
To generate the sequence y[n] = x[3*n], you would need to iterate over the elements of x[n] and select every third element.

Here is a code example in Python:

```python
x = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] # example sequence x[n]

y = [] # initialize sequence y[n]

for n in range(len(x)):
if n % 3 == 0: # select every third element
y.append(x[n])

print(y) # output: [1, 4, 7, 10]
```

In this example, the sequence x[n] is [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. The loop iterates over each element of x[n], and if the index n is divisible by 3 (i.e. n % 3 == 0), it adds the element to the sequence y[n]. The resulting sequence y[n] is [1, 4, 7, 10].
Community Answer
Given a sequence x[n], to generate the sequence y[n] = x[3 – 4n]...
In option 1,
z1[n] = x[n - 3]
z2[n] = z1[4n] = x[4n - 3]
y[n] = z2[-n] = x[-4n - 3] ≠ x[3 - 4n]
In option 2,
z1[n] = x[n + 3]
z2[n] =z1[4n] = x[4n + 3]
y[n] = z2[-n] = x[-4n + 3]
In option 3,
v1[n] = x[4n]
v2[n] = v1[-n] = x[-4n]
y[n] = v2[n+3] = x[-4(n + 3)] ≠ x[3 - 4n]
In option 4,
v1[n] = x[n]
x2[n] = v1[-n] = x[-4n]
y[n] = v2[n-3] = x[-4(n - 3)] ≠ x[3 - 4n]
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Given a sequence x[n], to generate the sequence y[n] = x[3 – 4n], which one of the following procedures would be correct?a)First delay x(n) by 3 samples to generate z1[n], then pick every 4th sample of z1[n] to generate z2[n], and than finally time reverse z2[n] to obtain y[n].b)advance x[n] by 3 samples to generate z1[n], then pick every 4th sample of z1[n] to generate z2[n], and then finally time reverse z2[n] to obtain y[n]c)First pick every fourth sample of x[n] to generate v1[n], time-reverse v1[n] to obtain v2[n], and then finally advance v2[n] by 3 samples to obtain y[n]d)First pick every fourth sample of x[n] to generate v1[n], time-reverse v1[n] to obtain v2[n], and finally delay v2[n] by 3 samples to obtain y[n]Correct answer is option 'B'. Can you explain this answer?
Question Description
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