Microwave Photonic Filters (MPFs) can find applications in the fields of optical communications, radar, optical fiber sensing. Due to the implementing of high-frequency optical signals and different optical processing devices, MPFs can achieve low loss, large bandwidth and compatible communication. To construct a finite impulse response MPF, researchers have proposed a variety of tapping and delay structures. An MPF can be classified as coherent one or incoherent one, according to the coherent characteristic of the adopted optical carriers. A simple approach of Phase-Modulation to Intensity-Modulation(PM-IM) conversion is usually used to construct a coherent MPF, but the frequency response of the MPF is limited by the adopted optical filter. The principle of the incoherent MPFs is based on the impulse response filters, which are constructed through multiple taps and time delays. One of the important indicators to evaluate the performance of the MPFs is the reconfigurability. In terms of tap implementation, using physical paths with equally spaced time delay is a common method, but this requires complicated switching structures to tune the length of each optical path. Another common approach is to use multi-wavelength sliced broadband optical sources or incoherent laser arrays, combined with dispersion fibers to achieve time delay. Usually, the positive coefficient MPFs require incoherent light sources to reduce interference between the adjacent taps, but it will increase the system noise. Therefore, how to achieve a high signal-to-noise ratio incoherent filter with tunable and reconfigurable performance is one of the critical issues that needs to be solved urgently in the field of microwave photonic signal processing.In this paper, an MPF with a simple structure and a high reconfigurability is demonstrated based on an optical Recirculating Frequency Shifting Loop (RFSL). By adding a Single-Sideband(SSB)modulator to an optical fiber loop, a new optical frequency component will be generated each time when the optical carrier passes through the SSB modulator which is modulated by a microwave signal. As a result, the proposed RFSL not only has an equally spaced comb-like spectrum in the frequency domain but also an equally spaced time delay between the adjacent optical carriers in the time domain. It can be found that a traditional MPF based on an RFSL mainly utilized its multi-carrier characteristics in the frequency domain and the time delay between the taps is achieved by using dispersive optical fibers. However, the time domain characteristics of the RFSL have not yet been effectively developed. In fact, the equally spaced time delay characteristic of the RFSL can be also used to introduce a time delay between different taps. Since the frequency difference between the multiple optical carriers generated by the RFSL is larger than the bandwidth of the photodetector, the intensity interference caused by the high coherence of the optical carriers can be avoided, and a stable spectral response can be achieved. By using a Programmable Optical Filter(POF) to shape the spectrum generated by the RFSL, different tap numbers can be controlled, and the weight of each tap can be precisely adjusted, thereby obtaining an effective tuning of the Free Spectral Range(FSR), tap number and weight.In the experiment, the output optical signal from the RFSL is delivered to the POF which is a Waveshaper, for spectral shaping. The POF provides a series of discrete frequency channels for the filtering of each carrier and modulation sideband of RFSL. After the k-th optical carrier is attenuated to a certain extent, any adjustable tap weight can be obtained. In terms of tunable reconfigurability, we propose to use the POF to change the delay between taps, and allocate new channels to each comb group (both carrier and sidebands) in the original RFSL. We experimentally demonstrated the switching of the tap number between 2, 5, and 10 with an FSR of 3.85 MHz, and the switching of the FSR between 3.85 MHz, 1.925 MHz, and 770 kHz with a tap number of 2. Through spectral shaping, we have achieved an MPF with a reconfiguration of the tap number and the FSR. Moreover, when the tap number is 5 or 10, the MPF with reconfigurable tap number has a Main to Secondary Sidelobe Ratio(MSSR)of 11 dB. On the other hand, the optical amplifier in the RFSL is an Erbium-Doped Fiber Amplifier(EDFA)which can bring a high small signal gain, the long erbium-doped fiber length will also increases the cavity length of the RFSL, which decreases the FSR in the experiment. The cavity length can be further reduced through using a Semiconductor Optical Amplifier(SOA), and other devices such as Polarization Controllers(PCs), Tunable Optical Filters(TOFs), pigtails and jumpers such as Dual-Parallel Mach-Zehnder Modulator(DPMZM)can all be optimized to reduce the optical length. Different from non-frequency-shifting loops, RFSL does not require much incoherence of the optical carrier source. Even under a small loop length, a stable multi-tap signal can still be obtained. Through further optimization, the FSR of the MPF we proposed can be increased to 100 MHz.