## Matched Filter Using Octave GNU Tool

### 3. Matched filter for chirp signal

##### See the Figure 3-1:

Figure 3-1: Chirp Signal

##### See the Figure 3-2:

Figure 3-2: Chirp Matched Filter Impulse Resonse

##### Now we send the signal (9) to the input of this filter and get the filter response, as shown in Figure 3-3. After receiving the chirp signal, the matched filter generates a short pulse. There are still lateral local maxima, the level of which is significantly lower than the main maximum.

Figure 3-3: Matched Filter Response on the Chirp Signal

### 4. Matched filter for Phase Shift Keying (PSK) with Barker Code

##### This sequence has a good autocorrelation function with a narrow peak. See the Figure 4-1

Figure 4-1: Autocorrelation function of the Barker code with the length 11

##### Now let’s build a PSK with Barker code. See the Figure 4-2:

Figure 4-2: PSK with the Barker code with the length 11

##### Using (1) the matched filter pulse response has the form shown in Figure 4-3

Figure 4-3: Matched Filter Impulse Response of the PSK with the Barker code

##### Then the reaction of the matched filter to this PSK signal sample shown in the Figure is 4-4:

Figure 4-4: Matched Filter Response on the PSK with the Barker code

##### Note:The PSK signal can be considered as a packet of radio pulses with phases 0 and π. Then we can build a matched filter for only one radio pulse and then use the tdelay time delay line for each subsequent radio pulse with a coefficient bi : +1 for the phase 0 and -1 for the phase π. See the Figure 4-5

Figure 4-5: PSK Matched Filter Using only One Radio Impulse S*one(jω)
where t_delay – one radio impulse time length

### 5. Matched filter for Maximum Length Sequence (MLS)

##### The polynomial can still be written as a binary number. In our example: 10000011, where bits: 7, 1, 0 have the values 1 (feedbacks are active) and all other bits have the values 0.

Figure 5-1: MLS: Feedback Shift Register

##### Now let’s build a Matched Filter for MLS using (1). The signal at the filter output after receiving the MLS is shown in Figure 5-2

Figure 5-2: Matched Filter Response on the MLS 10000011 sequence

• ##### There are many polynomials of different lengths that you can use to form the MLS sequence that suits you. The table of polynomials is easy to find in the special literature. See the few polynomials in the Table 5-1:

Table 5-1: MLS polynomials