> ## Documentation Index
> Fetch the complete documentation index at: https://docs.fincept.in/llms.txt
> Use this file to discover all available pages before exploring further.

# Fast Fourier Transform (Forward)

> Compute the Fast Fourier Transform of real-valued data, converting from time/spatial domain to frequency domain. FFT decomposes a signal into its constituent frequencies and is fundamental for signal processing, spectral analysis, convolution operations, and filtering. Returns complex-valued frequency components with real, imaginary, and magnitude values. [Tier: BASIC, Credits: 1]



## OpenAPI

````yaml api-specs/numerical.json post /quantlib/numerical/fft/forward
openapi: 3.1.0
info:
  title: FinceptQuantLib API - Numerical
  description: >-
    Numerical module endpoints for FinceptQuantLib API. The Numerical module
    (Basic Tier, 1 credit per request) provides comprehensive numerical methods
    including finite difference differentiation, Fast Fourier Transform (FFT),
    numerical integration (quadrature and Monte Carlo), interpolation methods
    (linear, cubic, spline), linear algebra operations (matrix decomposition,
    solving systems), ODE solvers, root finding algorithms, optimization
    methods, and nonlinear least squares fitting. Essential for quantitative
    analysis, scientific computing, and numerical model implementation.
  version: 3.0.0
  contact:
    name: Fincept API Support
    url: https://fincept.in
servers:
  - url: https://api.fincept.in
    description: Fincept API Production Server
security:
  - APIKeyHeader: []
tags:
  - name: quantlib-numerical
    description: >-
      Numerical methods including differentiation, FFT, integration,
      interpolation, linear algebra, ODE solvers, root finding, and optimization
    x-displayName: Numerical
paths:
  /quantlib/numerical/fft/forward:
    post:
      tags:
        - quantlib-numerical
      summary: Fast Fourier Transform (Forward)
      description: >-
        Compute the Fast Fourier Transform of real-valued data, converting from
        time/spatial domain to frequency domain. FFT decomposes a signal into
        its constituent frequencies and is fundamental for signal processing,
        spectral analysis, convolution operations, and filtering. Returns
        complex-valued frequency components with real, imaginary, and magnitude
        values. [Tier: BASIC, Credits: 1]
      operationId: fft_forward
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - data
              properties:
                data:
                  type: array
                  items:
                    type: number
                  description: Real-valued input data (time or spatial domain samples)
                  example:
                    - 1
                    - 2
                    - 3
                    - 4
                    - 4
                    - 3
                    - 2
                    - 1
            example:
              data:
                - 1
                - 2
                - 3
                - 4
                - 4
                - 3
                - 2
                - 1
      responses:
        '200':
          description: Successful Response
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      real:
                        type: array
                        items:
                          type: number
                        description: Real parts of FFT coefficients
                        example:
                          - 20
                          - -4.828
                          - 0
                          - -0.172
                          - 0
                          - -0.172
                          - 0
                          - -4.828
                      imag:
                        type: array
                        items:
                          type: number
                        description: Imaginary parts of FFT coefficients
                        example:
                          - 0
                          - 4.828
                          - 0
                          - 0.172
                          - 0
                          - -0.172
                          - 0
                          - -4.828
                      magnitude:
                        type: array
                        items:
                          type: number
                        description: Magnitude of each frequency component (absolute value)
                        example:
                          - 20
                          - 6.828
                          - 0
                          - 0.243
                          - 0
                          - 0.243
                          - 0
                          - 6.828
                      'n':
                        type: integer
                        description: Number of frequency components
                        example: 8
              example:
                success: true
                data:
                  real:
                    - 20
                    - -4.828
                    - 0
                    - -0.172
                    - 0
                    - -0.172
                    - 0
                    - -4.828
                  imag:
                    - 0
                    - 4.828
                    - 0
                    - 0.172
                    - 0
                    - -0.172
                    - 0
                    - -4.828
                  magnitude:
                    - 20
                    - 6.828
                    - 0
                    - 0.243
                    - 0
                    - 0.243
                    - 0
                    - 6.828
                  'n': 8
        '401':
          $ref: '#/components/responses/UnauthorizedError'
        '402':
          $ref: '#/components/responses/InsufficientTierError'
        '422':
          description: Validation Error
      security:
        - APIKeyHeader: []
components:
  responses:
    UnauthorizedError:
      description: Authentication information is missing or invalid
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Invalid API key
    InsufficientTierError:
      description: API tier insufficient for this endpoint
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Endpoint requires Basic tier or higher
  securitySchemes:
    APIKeyHeader:
      type: apiKey
      in: header
      name: X-API-Key
      description: >-
        API key for authentication. Get your key at
        https://api.fincept.in/auth/register

````