### Add fftea Dependency to pubspec.yaml

Source: https://pub.dev/packages/fftea/install

This is an example of how the fftea dependency will appear in your pubspec.yaml file after running the add command.

```yaml
dependencies:
  fftea: ^1.5.0+1
```

--------------------------------

### Import fftea Library in Dart Code

Source: https://pub.dev/packages/fftea/install

Import the fftea library into your Dart files to start using its functionalities.

```dart
import 'package:fftea/fftea.dart';
```

--------------------------------

### Run Spectrogram Viewer

Source: https://pub.dev/packages/fftea/example

Execute the command-line spectrogram viewer using Dart. This command processes an audio file to display its spectrogram via STFT.

```bash
dart run spectrogram.dart test.wav
```

--------------------------------

### Run a Basic Real-Valued FFT

Source: https://pub.dev/packages/fftea

Use this snippet to perform a real-valued Fast Fourier Transform on a list of doubles. Ensure the FFT object is constructed once and reused for performance. The result is a Float64x2List representing complex numbers.

```dart
import 'package:fftea/fftea.dart';

List<double> myData = ...;

final fft = FFT(myData.length);
final freq = fft.realFft(myData);

```

--------------------------------

### Add fftea to Flutter Project

Source: https://pub.dev/packages/fftea/install

Use this command to add the fftea package as a dependency in your Flutter project.

```bash
$ flutter pub add fftea
```

--------------------------------

### Add fftea to Dart Project

Source: https://pub.dev/packages/fftea/install

Use this command to add the fftea package as a dependency in your Dart project.

```bash
$ dart pub add fftea
```

--------------------------------

### Calculate Spectrogram using STFT

Source: https://pub.dev/packages/fftea

This snippet demonstrates how to compute a spectrogram using the Short-Time Fourier Transform (STFT). It processes audio data in chunks, applies a window function, and discards conjugate data and phase information for spectrogram representation. For optimal performance, consider using power-of-two chunk sizes.

```dart
import 'package:fftea/fftea.dart';

List<double> audio = ...;

final chunkSize = 1234;
final stft = STFT(chunkSize, Window.hanning(chunkSize));

final spectrogram = <Float64List>[];
stft.run(audio, (Float64x2List freq) {
  spectrogram.add(freq.discardConjugates().magnitudes());
});

```

--------------------------------

### Understanding FFT Result Redundancy

Source: https://pub.dev/packages/fftea

Illustrates the common practice of discarding conjugate data from real-valued FFT results to reduce redundancy, especially when generating spectrograms. The nyquist term is the last unique frequency component before the redundant conjugate terms begin.

```text
[sum term, ...terms..., nyquist term, ...conjugate terms...]
 ^----- These terms are kept ------^     ^- Discarded -^ 

```

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