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By Dahlquist G.

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The magnitude response is often expressed in decibels (dB) using the definition H( f ) dB = 20 log10 H ( f ) . , H ( f ) = H ∗(− f ). If the input and output signals are expressed in terms of power spectral density, then the input–output relation is given by 2 Sy ( f ) = H ( f ) Sx ( f ). The equations above show that an LTI system acts as a filter. Filters can be classified into lowpass, bandpass, and highpass filters and they are often characterized by stopbands, passband, and half-power (3 dB) bandwidth.

29) s (t ) 2 (t) and ϕ(t) = arctan Q where a(t) = s I2 (t) + s Q s I (t ) are both real-valued lowpass signals. 23). In the frequency domain the bandpass signal s(t) is represented by its Fourier transform ∞ S( f ) = −∞ ∞ = = 1 2 = 1 2 s(t)e− j 2π f t dt −∞ ∞ −∞ ∞ −∞ s(t)e j 2π f c t e− j 2π f t dt s(t)e j 2π f c t + s ∗ (t)e− j 2π f c t e− j 2π f t dt s(t)e− j 2π( f − fc )t dt + 1 2 ∞ −∞ s ∗ (t)e− j 2π( f + fc )t dt. 30) In the above derivation we used (v) = 12 (v + v ∗ ). 31) S( f ) = 12 S( f − f c ) + S ∗ (− f − f c ) .

The cross-correlation problem is solved by using very long codes. However, longer codes also delay the acquisition process. In most cases the processor must search at half-chip offsets; thus, 8184 possibilities for the L1 OS code. To search the very long code lengths proposed for the new signals would be impractical, so the codes have been designed with escape routes. The most common one is called a tiered code. This means it is built in layers so that when you have a strong signal you can acquire on a simple layer, with less time-domain possibilities, only switching to the full-length code when required.

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