Method and apparatus for zero-mixing spectrum analysis with Hilbert transform

• US 20060066290A1
• Filed: 09/27/2005
• Published: 03/30/2006
• Est. Priority Date: 09/27/2004
• Status: Active Grant

• Current Assignee: Rohde & Schwarz GmbH & Company KG
• Original Assignee: Rohde & Schwarz GmbH & Company KG
• Inventors: Hausdorf, Reiner, Baros, Pavel, Striz, Roman
• Granted Patent: US 7,176,670 B2
• Time in Patent Office: Days
• US Class Current: 324/76.270
• CPC Class Codes: G01R 23/165 using filters

Abstract

An apparatus (1) for analyzing a spectrum of an input signal (x(t)) having at least one line with a center frequency (ω_x) at the center of the line comprises:

a mixer (2) for zero-mixing the input signal (x(t)) to produce a base band signal (z(t)) by sweeping a local oscillator frequency (ω_s) generated by a local oscillator (3),

a resolution filter (4) for filtering the base band signal (z(t)) to produce a filtered base band signal (y(t)) and envelope reconstruction means (27) for reconstructing the envelope (E(ω)) of the spectrum of the input signal (x(t)) by using an estimated amplitude (ŷ_x) at an estimated center frequency ({circumflex over (ω)}_x) of each line of the input signal (x(t)). Only the reel component (I) of the base band signal (z(t)) is filtered with the resolution filter (4) and the imaginary component (Q) is generated from the filtered base band signal (y(t) by performing a Hilbert transform in a Hilbert filter (21) arranged downstream of the resolution filter (4).

Claims

1. Method for analyzing a spectrum of an input signal (x(t)) having at least one line with a center frequency (ω

_x) at the center of the line comprising the following steps;

zero-mixing the input signal (x(t)) to produce a base band signal (z(t)) by sweeping a local oscillator frequency (ω

_s),

filtering the base band signal (z(t)) with a resolution filter (4) to produce a filtered base band signal (y(t)),

reconstructing the envelope (E(ω

)) of the spectrum of the input signal (x(t)) by using an estimated amplitude (ŷ

_x) at an estimated center frequency ({circumflex over (ω

)}_x) of each line of the input signal (x(t)),

characterized in that

only the reel component (I) of the base band signal (z(t)) is filtered with the resolution filter (4) and the imaginary component (Q) is generated from the filtered base band signal (y(t)) by performing a Hilbert transform.

2. Method according to claim 1,

characterized in that

reconstructing the envelope (E(ω

)) of the spectrum of the input signal (x(t)) is done on the basis of the reel component (I) and on the basis of the imaginary component (Q) generated with the Hilbert transform.

3. Method according to claim 1 or 2,

characterized in that

the reel component (I) of the filtered base band signal (y(t)) is delayed by a delay time equivalent to the processing time of the Hilbert transform.

4. Method according to any of claims 1 to 3,

characterized in that

the amplitude values of the imaginary component (Q) generated by performing the Hilbert transform are corrected by an estimation on the basis of the neighbouring amplitude values of the reel component (I).

5. Method according to any of claims 1 to 4,

characterised in that

the Hilbert transform is performed by the use of a digital finite impulse response filter using the following coefficients

$h_n=\frac{1-e^{}}{}$

j⁢

 

⁢

n⁢

 

⁢

π

n⁢

 

⁢

π

,n≠

0,hn=0,n=0

wherein n is an index running from a first negative integer (−

M) to a second positive integer (+M) .

6. Method according to any of claims 1 to 5,

characterised in that

the estimated amplitude (ŷ

_x) and the estimated center frequency ({circumflex over (ω

)}_x) are calculated from the time of occurrence (t_i), the duration (Δ

T_i) and the maximum value (y_i) of at least one evaluated halfwave (10) of the reel component (I) and of the imaginary component (Q) of the filtered base band signal (y(t)).

7. Method according to claim 6,

characterized in that

the range of estimated individual values of the center frequency ({circumflex over (ω

)}_x,i) is divided into intervals (11a, 11b) for the reel component (I) and for the imaginary component (Q), the estimated individual values of the center frequency ({circumflex over (ω

)}_x,i) of all evaluated halfwaves (10) are related to these intervals (11a, 11b) giving a count for each estimated value of the center frequency ({circumflex over (ω

)}_x,i) falling within the respective interval (11a, 11b) and

the estimated individual values of the center frequency ({circumflex over (ω

)}_x,i) and the estimated individual amplitude values (ŷ

_x,i) at the centre frequency are averaged only for the interval(s) (11c) having a minimum number of counts in order to obtain the estimated center frequency ({circumflex over (ω

)}_x) and the estimated amplitude (ŷ

_x) at the estimated center frequency ({circumflex over (ω

)}_x).

8. Method according to claim 7,

characterized in that

the intervals (11a, 11b) overlap.

9. Apparatus (1) for analyzing a spectrum of an input signal (x(t)) having at least one line with a center frequency (ω

_x) at the center of the line comprising;

a mixer (2) for zero-mixing the input signal (x(t)) to produce a base band signal (z(t)) by sweeping a local oscillator frequency (ω

_s) generated by a local oscillator (3),

a resolution filter (4) for filtering the base band signal (z(t)) to produce a filtered base band signal (y(t)) and

envelope reconstruction means (27) for reconstructing the envelope (E(ω

)) of the spectrum of the input signal (x(t)) by using an estimated amplitude (ŷ

_x) at an estimated center frequency ({circumflex over (ω

)}_x) of each line of the input signal (x(t)),

characterized in that

only the reel component (I) of the base band signal (z(t)) is filtered with the resolution filter (4) and the imaginary component (Q) is generated from the filtered base band signal (y(t)) by performing a Hilbert transform in a Hilbert filter (21) arranged downstream of the resolution filter (4).

10. Apparatus according to claim 9,

characterized in that

in the envelope reconstruction means (27) the reconstruction of the envelope (E(ω

)) of the spectrum of the input signal (x(t)) is made on the basis of the reel component (I) and on the basis of the imaginary component (Q) generated by the Hilbert filter (21).

11. Apparatus according to claim 9 or 10,

characterized by

delay means (20) arranged parallel to the Hilbert filter (21) for delaying the reel component (I) of the filtered base band signal (y(t) by a delay time equivalent to the processing time of the Hilbert filter (21).

12. Apparatus according to any of claims 9 to 11,

characterized by

correction means (22) for correcting the amplitude values of the imaginary component (Q) generated by the Hilbert filter (21) by an estimation on the basis of the neighbouring amplitude values of the reel component (I).

13. Apparatus according to any of claims 9 to 12,

characterized in that

the Hilbert filter (21) is a digital finite impulse response filter using the following coefficients h_n

$h_n=\frac{1-e^{}}{}$

j⁢

 

⁢

n⁢

 

⁢

π

n⁢

 

⁢

π

,n≠

0,hn=0,n=0

wherein n is an index running from a first negative integer (−

M) to a second positive integer (+M).

14. Apparatus according to any of claims 9 to 13,

characterised by

detector means (23) for detecting the time of occurrence (t_i), the duration (Δ

T_i) and the maximum value (y_i) of at least one halfwave of the filtered base band signal (y(t)) and

translation means (24) wherein an estimated amplitude (ŷ

_x) and an estimated center frequency ({circumflex over (ω

)}_x) are calculated from the time of occurrence (t_i), the duration (Δ

T_i) and the maximum value (y_i) of at least one evaluated halfwave (10) of the reel component (I) and of the imaginary component (Q) of the filtered base band signal (y(t)).

15. Apparatus according to claim 14,

characterized by

classification means (25) wherein

the range of estimated individual values of the center frequency ({circumflex over (ω

)}_x,i) is divided into intervals (11a, 11b) for the reel component (I) and for the imaginary component (Q),

the estimated individual values of the center frequency ({circumflex over (ω

)}_x,i) of all evaluated halfwaves (10) are related to these intervals (11a, 11b) giving a count for each estimated value of the center frequency ({circumflex over (ω

)}_x,i) falling within the interval (11a, 11b) and

the estimated individual values of the center frequency ({circumflex over (ω

)}_x,i) and the estimated individual amplitude values (ŷ

_x,i) at the center frequency are averaged only for the interval(s) (11c) having a minimum number of counts in order to obtain the estimated center frequency ({circumflex over (ω

)}_x) and the estimated amplitude (ŷ

_x) at the estimated center frequency ({circumflex over (ω

)}_x).

16. Apparatus according to claim 15,

characterised in that

the intervals (11a, 11b) overlap.