Pengolahan Sinyal Digital: 09 Transformasi Fourier, STFT & Wavelet Transform

Summary

In this video, the concept of digital signal processing is explored, focusing on the challenges faced in analyzing signals over time. The discussion covers Fourier Transform, Short-Time Fourier Transform (STFT), and Wavelet Transform. The video explains how traditional Fourier Transform struggles with signals that change frequency over time, and how STFT and Wavelet Transform offer solutions by analyzing signals in smaller time segments. The importance of selecting appropriate windows for analysis and understanding frequency changes across time is emphasized, with examples including signals like speech and heartbeats. The tutorial also discusses different window functions and the role of scaling in signal analysis.

Takeaways

• 😀 The Fourier Transform is useful for periodic signals but struggles with signals whose frequency changes over time.
• 😀 The Short-Time Fourier Transform (STFT) can analyze signals by breaking them into smaller time segments, improving time-frequency resolution.
• 😀 STFT helps observe how the frequency content of a signal evolves over time, addressing the issue of varying frequencies.
• 😀 Window functions like Hamming, Hanning, and others shape the time-frequency resolution of the STFT and influence signal analysis.
• 😀 Wavelet Transform is an alternative to STFT, offering more flexible time-frequency resolution by using varying scales.
• 😀 In STFT, the signal is analyzed in 'windows,' with the window size impacting the frequency and time resolution.
• 😀 The frequency spectrum observed in STFT can show how a signal's frequency shifts over time, such as from low to high frequencies.
• 😀 The time-domain signal can be transformed into a time-frequency domain with STFT, making it easier to observe frequency changes.
• 😀 Wavelet Transform differs from STFT by using wavelets of different scales, which allows for better adaptability to varying signal structures.
• 😀 Analyzing signals in terms of both time and frequency helps identify changes in the signal that may not be clear in one domain alone.

Q & A

What is the main focus of the video on digital signal processing?

The video focuses on discussing issues related to digital signal processing, specifically short-time Fourier transform (STFT) and wavelet transform, and how they can be used to analyze signals that change over time.

What problem is highlighted with the Fourier transform when analyzing a signal?

The problem with Fourier transform is that it fails to capture the time-varying frequency changes of a signal. For example, if a signal has a frequency that shifts over time, the Fourier transform will show the same frequency components, even though the actual frequency is changing.

How does the Short-Time Fourier Transform (STFT) address the limitations of the Fourier transform?

STFT addresses these limitations by analyzing the signal in small overlapping windows over time. This allows for tracking how the frequency content of the signal evolves, providing a time-frequency representation of the signal.

What role does the window function play in Short-Time Fourier Transform?

The window function in STFT is used to isolate a small portion of the signal for analysis. By shifting the window across the signal, the STFT provides insights into how the frequency content of the signal changes over time.

What are some examples of window functions mentioned in the video?

Examples of window functions mentioned include Hamming, Blackman-Harris, and other common types that follow a bell-shaped curve. These window functions are important for controlling the resolution and smoothness of the time-frequency analysis.

What is the difference between Fourier transform and Wavelet transform in signal analysis?

While Fourier transform analyzes the signal based on sine and cosine functions, the Wavelet transform allows for variable resolution in both time and frequency, making it more effective in analyzing signals with non-stationary or time-varying characteristics.

How does the Wavelet transform differ in its approach to time-frequency analysis compared to STFT?

The Wavelet transform differs by using wavelets that are not fixed in size. Unlike STFT, where the window size remains constant, the wavelet transform adjusts the scale of the analysis window based on the frequency of the signal, offering better resolution for varying frequencies.

What does the video say about analyzing speech signals in terms of frequency shifts over time?

The video explains that speech signals, like 'Hello, how are you?', show varying frequency components over time. For example, low frequencies might dominate at certain times, while high frequencies appear at other moments, which can be captured effectively using STFT or wavelet transforms.

Why is it important to analyze signals over time when using these transforms?

It is important to analyze signals over time because many real-world signals, like speech or music, have frequencies that change continuously. By observing how the frequency content evolves, we can better understand the signal’s characteristics and behaviors at different moments.

What is meant by 'time-frequency domain' in the context of these signal processing techniques?

The 'time-frequency domain' refers to a representation where both time and frequency are considered simultaneously. This allows for better visualization of how the frequency content of a signal changes over time, which is essential for analyzing dynamic signals.