The number of butterflies required per output point in the FFT (Fast Fourier Transform) algorithm is given by N-1, where N is the number of samples in the input signal.

Explanation:

1. What is the FFT algorithm?
The FFT algorithm is a fast and efficient method for calculating the Discrete Fourier Transform (DFT) of a sequence. It is widely used in various applications such as signal processing, image processing, and data compression.

2. How does the FFT algorithm work?
The FFT algorithm recursively divides the DFT computation into smaller sub-problems. It utilizes the concept of "butterflies" to combine the results of these sub-problems and obtain the final DFT output.

3. What is a butterfly in the FFT algorithm?
In the FFT algorithm, a butterfly refers to a pair of complex multiplications and additions. It takes two complex numbers as input, performs the operations, and produces two output complex numbers.

4. How many butterflies are required in the FFT algorithm?
The number of butterflies required in the FFT algorithm depends on the size of the input sequence. For a sequence of N samples, there are N/2 butterflies at the first stage of the algorithm. At each subsequent stage, the number of butterflies reduces by half.

5. Calculation of butterflies per output point:
To calculate the number of butterflies per output point, we need to consider the number of stages in the FFT algorithm. The number of stages is given by log2(N), where N is the number of samples in the input sequence.

At each stage, the number of butterflies is halved. Therefore, the number of butterflies per output point is N/2 at the first stage, N/4 at the second stage, N/8 at the third stage, and so on.

6. Final calculation:
To obtain the total number of butterflies per output point, we sum up the number of butterflies at each stage. This can be represented as:

N/2 + N/4 + N/8 + ... + 1

Using the formula for the sum of a geometric series, the above expression simplifies to:

N * (1/2 + 1/4 + 1/8 + ... + 1/N)

This sum converges to 1 as N approaches infinity. Therefore, the number of butterflies per output point can be approximated as N-1.

Conclusion:
In conclusion, the number of butterflies required per output point in the FFT algorithm is N-1, where N is the number of samples in the input signal. This calculation takes into account the recursive nature of the algorithm and the reduction in the number of butterflies at each stage.