https://github.com/maximilianfeldthusen/fftw

This C++ code generates a sample signal composed of a sine wave with added noise, performs a Fast Fourier Transform (FFT) on that signal, and then displays the magnitude spectrum of the FFT result.
https://github.com/maximilianfeldthusen/fftw

cpp fft signal

Last synced: 4 months ago
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This C++ code generates a sample signal composed of a sine wave with added noise, performs a Fast Fourier Transform (FFT) on that signal, and then displays the magnitude spectrum of the FFT result.

• Host: GitHub
• URL: https://github.com/maximilianfeldthusen/fftw
• Owner: maximilianfeldthusen
• License: bsd-3-clause
• Created: 2025-03-10T06:00:52.000Z (7 months ago)
• Default Branch: TFD
• Last Pushed: 2025-04-18T07:46:54.000Z (6 months ago)
• Last Synced: 2025-04-18T21:38:02.181Z (6 months ago)
• Topics: cpp, fft, signal
• Language: C++
• Homepage:
• Size: 16.6 KB
• Stars: 5
• Watchers: 1
• Forks: 1
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          

## Documentation

### **Overview**

This program generates a synthetic signal composed of a sine wave with added noise, computes its Fast Fourier Transform (FFT) to analyze its frequency components, detects peaks in the spectrum, and displays the results.

---

### **Included Libraries**

- ``: for input/output operations.

- ``: to handle dynamic arrays.

- ``: for complex number operations (though not directly used here).

- ``: FFTW library for performing FFTs.

- ``: mathematical functions like `sin()` and `sqrt()`.

- ``, ``, ``: for random number generation.

- ``: for functions like `max_element()`.

---

### **Constants and Data Structures**

- `PI`: a constant for π.

- `struct Peak`: to store information about detected peaks (their index and magnitude).

---

### **Functions**

#### 1. `generateSignal()`

- **Purpose:** Creates a synthetic signal of length `N` samples containing a sine wave of a specified frequency (`freq`) plus random noise.

- **Parameters:**

  - `N`: number of samples.

  - `freq`: sine wave frequency.

  - `sampleRate`: sampling rate in Hz.

  - `generator`: random engine for noise.

  - `noiseAmplitude`: amplitude of added noise (default 0.5).

- **Process:**

  - For each sample `n`, compute `sin(2π * freq * n / sampleRate)`.

  - Add random noise uniformly distributed between -0.5 and 0.5, scaled by `noiseAmplitude`.

- **Returns:** a vector containing the noisy sine wave.

---

#### 2. `performFFT()`

- **Purpose:** Computes the FFT of the input signal and returns the magnitude spectrum.

- **Process:**

  - Allocates memory for FFT input (`in`) and output (`out`) arrays using FFTW.

  - Copies the real input signal into the complex input array (`in`), setting imaginary parts to zero.

  - Creates an FFT plan and executes it.

  - Calculates the magnitude of the first half of the FFT output (since the FFT of real signals is symmetric).

  - Frees FFTW resources.

- **Returns:** a vector of magnitudes representing the spectrum.

---

#### 3. `detectPeaks()`

- **Purpose:** Finds local maxima in the spectrum that are above a specified threshold.

- **Parameters:**

  - `spectrum`: magnitude spectrum.

  - `threshold`: minimum magnitude to consider a peak.

  - `minDistance`: minimum separation between peaks (not fully implemented here).

- **Process:**

  - Iterates through the spectrum (excluding first and last points).

  - Checks if a point is greater than its neighbors and above the threshold.

  - Collects such points as peaks.

- **Returns:** a vector of `Peak` objects.

---

#### 4. `displaySpectrum()`

- **Purpose:** Prints a summarized view of the spectrum, limiting the number of printed points for readability.

- **Parameters:**

  - `spectrum`: the magnitude spectrum.

  - `maxPoints`: maximum number of points to display (default 50).

---

#### 5. `displayPeaks()`

- **Purpose:** Prints information about the detected peaks.

---

### **Main Function Workflow**

1. **Initialize Random Generator:**

   - Seeds with current time for noise randomness.

2. **Parameters:**

   - `sampleRate = 1024 Hz`

   - `N = 1024 samples`

   - `freq = 50 Hz` (signal frequency)

3. **Generate Signal:**

   - Calls `generateSignal()` to create a noisy sine wave.

4. **Compute FFT:**

   - Calls `performFFT()` to get the spectrum.

5. **Display Spectrum:**

   - Calls `displaySpectrum()` to print a summarized spectrum.

6. **Peak Detection:**

   - Finds the maximum magnitude in the spectrum.

   - Sets a threshold at 30% of this maximum.

   - Calls `detectPeaks()` to find peaks above this threshold.

7. **Display Detected Peaks:**

   - Calls `displayPeaks()`.

---

### **Summary**

This code performs a basic spectral analysis:

- Generates a noisy sine wave signal.

- Uses FFT to analyze its frequency content.

- Detects prominent peaks in the spectrum, which correspond to significant frequency components.

- Outputs the spectrum and the peaks for inspection.

This approach is common in signal processing applications for identifying dominant frequencies in noisy signals.

---

**Note:** To run this code, you need to have FFTW installed on your system and compile with the appropriate flags, e.g., `-lfftw3`.