Given x[n] = {1.5, 1, 0, −1.5, 2.5, 1,−1} with origin at -1.5. Find the signal transformationsapplied to x[n] to get y[n] = {−1, 2.5, 0, 1.5} with origin at -1.

To obtain the signal transformation applied to x[n] to get y[n], we need to perform the following steps:

1. Shifting the origin: Since the origin of x[n] is at -1.5, we need to shift it to -1 to match the origin of y[n]. This can be done by adding 0.5 to each index of x[n]. The shifted signal, let's call it x_shifted[n], is given by: x_shifted[n] = x[n + 0.5]

2. Truncating the signal: The signal y[n] has fewer elements than x_shifted[n]. To obtain y[n], we need to remove the extra elements from x_shifted[n]. Since y[n] starts at -1, we need to remove the first two elements of x_shifted[n]. The truncated signal, let's call it x_truncated[n], is given by: x_truncated[n] = x_shifted[n - 2]

3. Reversing the signal: The signal y[n] is in reverse order compared to x_truncated[n]. To reverse the signal, we need to flip the elements of x_truncated[n]. The reversed signal, let's call it x_reversed[n], is given by: x_reversed[n] = x_truncated[-n]

4. Shifting the origin again: Finally, we need to shift the origin of x_reversed[n] back to -1. This can be done by subtracting 1 from each index of x_reversed[n]. The shifted signal, let's call it x_final[n], is given by: x_final[n] = x_reversed[n - 1]

After performing these signal transformations on x[n], we obtain y[n] = {-1, 2.5, 0, 1.5} with the origin at -1.