# US 9,438,277 B2 · Intermediate frequency spectral placement of bandpass sampled signals

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- Number: US 9,438,277 B2
- Document ID: US9438277B2
- Status: Granted
- Kind: B2
- Application number: 14/452,042
- Filed: 2014-08-05
- Published: 2016-02-11
- Granted: 2016-09-06
- Earliest claimed: 2014-08-05
- Assignees: The United States of America as represented by the Secretary of the Navy
- Applicants: Sunil Ramlall; Rohan Ramlall
- Inventors: Sunil Ramlall; Rohan Ramlall
- Web page: https://patentgrep.com/patent/US9438277B2

## CPC

- H04B 1/0007: {wherein the AD/DA conversion occurs at radiofrequency or intermediate frequency stage}
- H03M 1/1255: {Synchronisation of the sampling frequency or phase to the input frequency or phase}
- H04L 5/001: {the frequencies being arranged in component carriers}
- H04B: TRANSMISSION
- H03M: CODING; DECODING; CODE CONVERSION IN GENERAL (using fluidic means F15C4/00; optical analogue/digital converters G02F7/00; coding, decoding or code conversion, specially adapted for particular applications, see the relevant subclasses, e.g. G01D, G01R, G06F, G06T, G09G, G10L, G11B, G11C, H04B, H04L, H04M, H04N; ciphering or deciphering for cryptography or other purposes involving the need for secrecy G09C)
- H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M)

## Abstract

Systems and methods for bandpass sampling of a continuous analog signal according to several embodiments can use a linear relationship between sampling frequency and intermediate frequency f IF = ( - 1 ) n + 1 ⁢ ( - ⌊ n 2 ⌋ ⁢ F S ⁢ + f C ) where fIF is the intermediate frequency and FS is the sampling frequency of the bandpass sampling, fC is the carrier frequency, B is a bandwidth and fU is an upper frequency for the signal, and n is an integer such that 1 ≤ n ≤ ⌊ f U B ⌋ . The sampling frequency FS can be chosen first and the IF can be calculated without iteration using the relationship above. Or, when fIF is the most important design parameter, fIF can be selected first, and sample frequencies which will not cause aliasing can be solved by calculating FS given IF using the equation above, for all values of n so that 1 ≤ n ≤ ⌊ f U B ⌋ , and then selecting a particular FS. fIF can be chosen to be FS/4.

## Claims

### Claim 1

A method for analog to digital conversion using bandpass sampling of a continuous analog signal, said method comprising the steps of:
A) providing a software-defined radio (SDR) including an analog to digital converter (ADC) having a sampling frequency FS;
B) choosing an intermediate frequency fIF;
C) solving for
⌊
f
U
B
⌋
possible said sampling frequencies using the relationship
F
S
=
(
-
1
)
n
+
1
⁢
f
IF
-
f
C
-
⌊
n
2
⌋
⁢
⁢
n
=
1
,
…
⁢
,
⌊
f
U
B
⌋
where fIF is said intermediate frequency, FS is said sampling frequency, fC is the carrier frequency for said signal, B is the bandwidth of said signal, fU is the upper frequency defined to be
f
U
=
f
C
+
B
2
of said signal, n is an integer such that
1
≤
n
≤
⌊
f
U
B
⌋
,
and └ ┘ denotes the mathematical floor function;
D) verifying at least one said FS from said step C) is valid by checking if each said FS from said step C) satisfies
2
⁢
⁢
f
U
n
≤
F
S
≤
2
⁢
⁢
f
L
n
-
1
where fL is the lower frequency defined to be
f
L
=
f
C
-
B
2
of said signal;
E) selecting a valid said at least one FS from said step D) for said bandpass sampling, without iterating fIF;
F) setting said sampling frequency of said ADC, by said SDR, at said at least one FS from said step E); and
G) using said ADC to bandpass sample said continuous analog signal.

### Claim 2 (depends on 1)

The method of claim 1, wherein said fIF from said step B) is FS/4.

### Claim 3 (depends on 1)

The method of claim 1, wherein said signal is a digital communication signal having a symbol rate and said FS from said step E) is an integer multiple of the symbol rate.

### Claim 4

A system comprising:
a software-defined radio (SDR) including an analog to digital converter (ADC) having a sampling frequency FS;
said ADC using a predetermined intermediate frequency fIF;
said SDR setting said sampling frequency FS of said ADC, without iteration of said fIF, based on the relationship
f
IF
=
(
-
1
)
n
+
1
⁢
(
-
⌊
n
2
⌋
⁢
F
S
+
f
C
)
,
where fC is a carrier frequency and fU is an upper frequency for said signal, where B is the bandwidth, and where n is an integer such that
1
≤
n
≤
⌊
f
U
B
⌋
and └ ┘ denotes the mathematical floor function; and
said ADC accomplishing analog to digital conversion using bandpass sampling of a continuous analog signal at said sampling frequency FS.