> ## 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.

# Inverse Fast Fourier Transform

> Compute the inverse FFT to transform frequency domain data back to time/spatial domain. Used to reconstruct signals after frequency domain processing, filtering, or convolution operations. Input is treated as real values representing complex numbers with zero imaginary parts. [Tier: BASIC, Credits: 1]



## OpenAPI

````yaml api-specs/numerical.json post /quantlib/numerical/fft/inverse
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/inverse:
    post:
      tags:
        - quantlib-numerical
      summary: Inverse Fast Fourier Transform
      description: >-
        Compute the inverse FFT to transform frequency domain data back to
        time/spatial domain. Used to reconstruct signals after frequency domain
        processing, filtering, or convolution operations. Input is treated as
        real values representing complex numbers with zero imaginary parts.
        [Tier: BASIC, Credits: 1]
      operationId: fft_inverse
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - data
              properties:
                data:
                  type: array
                  items:
                    type: number
                  description: Frequency domain data (real parts, imaginary assumed zero)
                  example:
                    - 20
                    - -4.828
                    - 0
                    - -0.172
                    - 0
                    - -0.172
                    - 0
                    - -4.828
            example:
              data:
                - 20
                - -4.828
                - 0
                - -0.172
                - 0
                - -0.172
                - 0
                - -4.828
      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 reconstructed time-domain signal
                        example:
                          - 1
                          - 2
                          - 3
                          - 4
                          - 4
                          - 3
                          - 2
                          - 1
                      imag:
                        type: array
                        items:
                          type: number
                        description: Imaginary parts (typically near zero for real signals)
                        example:
                          - 0
                          - 0
                          - 0
                          - 0
                          - 0
                          - 0
                          - 0
                          - 0
                      'n':
                        type: integer
                        description: Number of time-domain samples
                        example: 8
              example:
                success: true
                data:
                  real:
                    - 1
                    - 2
                    - 3
                    - 4
                    - 4
                    - 3
                    - 2
                    - 1
                  imag:
                    - 0
                    - 0
                    - 0
                    - 0
                    - 0
                    - 0
                    - 0
                    - 0
                  '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

````