Title:
Apparatus for transforming electronics signals between the time and frequency domains utilizing acoustic waves
United States Patent 3925653
Abstract:
Apparatus for transforming electronic signals between the time domain and frequency domain in real time which comprises means for mixing the signal to be transformed with a predetermined chirp (variable frequency signal) in an acoustic wave convolver.
Application Number:
05/434965
Publication Date:
12/09/1975
Assignee:
The Board of Trustees of Leland Stanford Jr. University (Stanford, CA)
Other Classes:
324/76.22, 324/76.23, 333/154, 333/193
International Classes:
G06G7/195; G06G7/00; (IPC1-7): G06G7/19; H01L41/00
Field of Search:
235/181,193 310
Primary Examiner:
Gruber, Felix D.
Attorney, Agent or Firm:
Fihe, Paul B.
Claims:
What is claimed is
1. Apparatus for transforming an electronic signal between the time and frequency domain which comprises
2. Apparatus for transforming an electronic signal according to claim 1 wherein
3. Apparatus for transforming an electronic signal according to claim 1 which comprises
4. Apparatus for transforming an electronic signal according to claim 1 wherein
Description:
FIELD OF THE INVENTION
The present invention relates to the processing of electronic signals and more particularly to apparatus for transforming signals between the time and frequency domains through utilization of acoustic waves.
BACKGROUND OF THE INVENTION
It has been observed that a Fresnel transformation takes the mathematical form of convolution and moreover that initial multiplication of a signal by a complex chirp, then a Fresnel transformation, (convolution) and finally multiplication by a complex chirp provides a Fourier transformation. For example, L. Mertz has discussed this transformation relationship in "Transformations in Optics" (Wiley 1965) at pages 83 and 94.
The operation of convolution (and correlation) has been carried out through the parametric interaction of acoustic waves as explained in U.S. Pat. No. 3,760,172 issued Sept. 18, 1973, to Calvin F. Quate, and a large number of additional acoustic convolvers have been developed such as described in the Otto article entitled "Lithium-Niobate Silicon Surface Wave Convoluter" in ELECTRONICS LETTERS, Volume 8, No. 24.
SUMMARY OF THE PRESENT INVENTION
It is the general objective of the present invention to provide apparatus for transforming an electronic signal between the time and frequency domain (e.g. Fourier transform) through utilization of suitable signal mixing and acoustic wave convolution.
Such objective is achieved generally through the mixing of the signal to be transformed with a complex chirp, thus to correspond to the mathematical multiplication mentioned hereinabove. The mixing means can take the form of a conventional electronic signal mixer. The mixed signal can be applied through a suitable transducer to generate an acoustic signal in a piezoelectric medium arranged to provide a convolution operation equivalent to the mentioned Fresnel transformation. Finally, means to provide a final mixing of the convoluted output with a chirp produces the final multiplication operation and the ultimate completed transformation.
BRIEF DESCRIPTION OF THE DRAWING
The stated objective of the invention and the manner in which it is achieved, as summarized hereinabove, will be more fully understood by reference to the following detailed description of the exemplary apparatus depicted in the accompanying drawing wherein the single FIGURE constitutes a diagrammatic showing of electro-acoustic apparatus for obtaining the Fourier Transform of an arbitrary electronic signal.
DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENT OF THE INVENTION
As illustrated diagrammatically, the input modulated electronic signal to be transformed at a R.F. frequency ω, is delivered to a conventional radio frequency mixer 14.
A tunable radio frequency chirp generator 12 is arranged to generate a chirp signal at a frequency ω-ω1 +δ with a linear frequency ramp which may extend over a frequency range δ of 18 MHz and have an overall pulse length sufficient to encompass the length of the input signal, and the chirp signal is also delivered to the mixer 14 which performs the electronic analogue of the mentioned multiplication and the mixed signals are delivered at the sum frequency, ω+δ, (e.g. 200 MHz) to an electro-acoustic interdigital transducer 18 on the surface of a piezoelectric medium 16 so as to generate an acoustic wave which travels to the right as viewed in the FIGURE. Such form of transducer and acoustic wave generation are discussed in more detail in U.S. Pat. application, Ser. No. 190,342 now U.S. Pat. No. 3,816,753, entitled "Parametric Acoustic Surface Wave Apparatus" to which reference is made for such details.
The R.F. chirp signal is also delivered to a time inverter 20 which essentially reverses the slope of its linear frequency ramp so that the chirp frequency is now ω-ω1 -δ. The time inverter 20 may be an acoustic inverter as described in detail in the mentioned U.S. Pat. application Ser. No. 190,342. Alternatively, the time inverted chirp may be generated by the common technique of spectral inversion of the original chirp. The inverted chirp is applied to another mixer 19 together with a continuous radio frequency signal at ω1, from a tunable generator 21, to develop a mixed output at a frequency, ω-δ. This mixed signal is then applied to the opposite end of the piezoelectric medium 16 through another interdigital transducer 22 so to generate an acoustic wave which travels to the left as viewed in the FIGURE and because of such opposite direction of travel, the R.F. chirps from the left and right transducers will have equivalent configurations in the piezoelectric medium.
Frequency conservation and phase matching conditions between the two acoustic signals are attained within the piezoelectric medium 16 so that parametric interaction occurs as explained in some detail in the mentioned U.S. Pat. No. 3,760,172 and the acoustic energy is extracted by an acoustic detector 24 in the form of plates on the upper and lower surfaces of the piezoelectric medium 16 to provide the convolution of the two signals, which, in turn, as previously mentioned, provides a Fresnel transformation. The convolution operation provides addition of the basic radio frequencies and because of the opposite signal propagation, quadruples the chirp slope, thus providing an output signal at 2ω+4δ. The detector (plate) length is greater than the length occupied by the signal so that the entire signal will undergo the parametric interaction.
The final "multiplication" is provided by a mixer 28 that combines the convoluted output at frequency 2ω+4δ with another chirp which can, in the present instance, be readily obtained by quadrupling the frequency with a conventional frequency quadrupler 26 of the generated R.F. input chirp mixed in another mixer 30 with the continuous wave signal from the c.w. radio frequency generator 21 to provide a frequency 4ω+4δ. The output of the mixer 28 is then the Fourier Transform of the input signal at a frequency 2ω and it is to be particularly observed that such output is obtained in real time.
Various modifications can obviously be made in the structure as described to perform the necessary steps of chirp multiplication, Fresnel transformation (convolution) and final chirp multiplication. For example, the illustrated device utilized acoustic surface waves and the operation can as well be carried out with bulk acoustic waves as described in the mentioned U.S. Pat. No. 3,760,172. Furthermore, any other form of acoustic convolver can be utilized. Consequently, the foregoing description is not to be considered as limiting and the actual scope of the invention is only to be indicated by the appended claims.