## Problem Implement a causal moving-average filter that smooths a noisy 1D signal. Given an input array and a window size W, replace each sample with the mean of the W most recent samples (including the current one). Handle the boundary at the start of the signal. ```python def moving_average(signal: list[float], window: int) -> list[float]: # Causal: output[i] = mean(signal[max(0,i-window+1) : i+1]) pass def moving_average_fast(signal: list[float], window: int) -> list[float]: # O(n) using a running sum; no recomputation per window pass ``` **Example:** ``` moving_average([1,3,5,7,9], window=3) -> [1.0, 2.0, 3.0, 5.0, 7.0] # Index 0: mean([1])=1, Index 1: mean([1,3])=2, Index 2: mean([1,3,5])=3 ... ``` ## Follow-ups 1. What is the time complexity of the naive vs. running-sum approach? 2. How does a Gaussian filter differ from a box (moving-average) filter in the frequency domain? 3. How would you implement an exponential moving average (EMA) for real-time streaming data? 4. How would you extend this to a 2D image smoothing filter?

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Smoothing Filter: Implement a 1D Moving-Average Smoothing Filter on a Signal

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Problem Implement a causal moving-average filter that smooths a noisy 1D signal. Given an input array and a window size W, replace each sample with the mean of the W most recent samples (including the current one). Handle the boundary at the start of the signal. Example: Follow-ups What is the time complexity of the naive vs. running-sum approach? How does a Gaussian filter differ from a box (moving-average) filter in the frequency domain? How would you implement an exponential moving average (E…

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It covers the following topics: Arrays, Coding, Phone .

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Smoothing Filter: Implement a 1D Moving-Average Smoothing Filter on a Signal

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